Warmup 8-17(Geom) Add or subtract each set of polynomials. Answers should be in standard form. Show...

Warmup 8-17(Geom)

Add or subtract each set of polynomials. Answers should be in standard form.Show work!

1. (16x - 7x3 + 13) - (19x3 + 23 - 41x)

Multiply the polynomials below. Show work!

2. (3x - 2)(4x2 – 5x - 1)

Use the rules of exponents to simplify the following expressions.

3. (5x3y2)(-9x5y-4)

4. (-3x-3y4)-2

Examples of Rational/Irrational #’s,Perfect Squares and Factors(Geom)

Identify whether each number below is rational or irrational. 1. ½ 2. √5 3. √16

4. -1/3 5. 6.825 6. π

7. √12 8. 1 +√80 9. 3√8

What makes a number a perfect square? Why is the word “square” used?

Determine the perfect square values for the integers 0-15.

List all factors for the following numbers:8. 28 2. 32 3. 60

4. 72 5. 84 6. 100

Make a factor tree for the following numbers:5. 40 2. 56 3. 80

4. 96 5. 120

Rational vs. Irrational #’s,Perfect Squares and Factor Practice(Geom)

Identify whether each number below is rational or irrational. Explain. 1. √11 2. 3π 3. √81

4. -4/5 5. .8125 6. 5 + √121

7. π/4 8. 4 +√6 9. 8√12

10. 7√25

Determine if the following numbers are perfect squares. Show why. 11.144 12. 288 13. 48

14. 324 15. 900 16. 120

Make a factor tree for the following numbers:17. 45 18. 60 19. 88

20.80 21. 96 22. 100

23. 150 24. 144

Ticket out the Door 8-17(Geom)

Identify whether each number below is rational or irrational. Explain. 1. 14 -√121 2. π/6 3. 7√5 4. 1.0025

Determine if the following numbers are perfect squares. Show why. 5. 169 6. 80

Make a factor tree for the following numbers:7. 54 8. 64

Warmup 8-19(Geom)

Add or subtract the polynomials below.Show work!

1. (13x3 – 4x4 + 9x2) – (11x2 – 19x4 + 7x)


2. -18x-4y6 3. (5x2y-3)2

45xy2

4. Tell whether the following expressions are examples of rational or irrational numbers. a. 11π b. 2 + √49

Warmup 8-24(Geom)


1. (-5x9y-7)(9x-5y-2)

2. Tell whether the following expressions are examples of rational or irrational numbers. a. 5√144 b. 9 + √37

3. Simplify: √(90x2y)

4. Add or subtract: √80 - 3√48 + 2√75 - 4√125

Warmup 8-21(Geom)

Use the rules of exponents to simplify the following expressions. No negative exponents in the answers.

1. (6x-3y4)(-11x7y-8)

2. -20x5y-3

28x-4y-1

3. Simplify:√(64x3y4)

4. Tell whether the following expressions are examples of rational or irrational numbers. a.5√144 b. 9 + √37

Warmup 8-25(Geom)

Use the rules of exponents to simplify the following expressions. No negative exponents in the answers.

1. (8x5y-3)(-6x-2y-7)

2. 25x-7y-5

30x4y-9

3. (2x-4y8)5

4. Simplify: √(60x6y3)

GeometryMini Quiz

Rationals, Irrationals, Radicals, and Exponent Rules

Tell whether the following expressions are examples of rational or irrational numbers. 1. 11 - 2π 2. 7√25

Simplify each radical expression below. Show work!

3. √(28xy2) 4. √(49x4y6.)

5. √(96xy3)

Combine like terms in the following radical expressions. Show work!

6. 2√96 - √90 - 3√40 7. 4√28 - 5√44 + √63 + 2√99

Use exponent rules to simplify the following expressions. No negative exponents!

8. (-5x9y-7)(9x-5y-2) 9. (3x-4y6)5

10. -14x-3y4 11. (-5) -7 × (-5) 4

20x-8y-2

Examples Greatest Common Factor

8-21(Geom)Factor the GCF out of each polynomial. Show work!

1. 6x – 48 2. 14x3 – 39x2

3. 16x2 – 24x – 40 4. 10x2y + 25xy2 – 30x3

5. 27x2y2 + 9xy - 36x2y3

6. 36x3y2 – 60x2y2 - 24x2y

Ticket Out the Door 8-24(geom.) (Greatest Common Factor)

Factor the GCF out of each polynomial. Show work!

1. 18x2 – 27x + 45

2. 32x2y + 56xy2 – 16y3

3. 35x3y2 – 7xy + 63x2y3

4. 24x2y3 – 15x2y2 + 10x2y

Warmup 8-27

1. Add or Subtract:3√(80) - 2√(72) - √(125) - 4√(50)

Factor the GCF out of each polynomial. Show work!

2. 32x3y - 40x2y2

3. 27x2y - 9xy2 - 54x2y2

Warmup 8-28Factor the following equations completely. Show work!

1. x2 – 8x - 84

2. x2 - 18x + 81

3. 15x3y2 – 36x2y

4. 6x2 - 12x - 90

Ticket Out the Door 8-28 Factoring A>1, with GCF

Factor the following equations completely. Show work!

1. 2x2 – 6x – 9 2. 5x2 – 14x + 8

3. 6x2 + 33x + 42 4. 3x2 + 9x – 10

Warmup 8-31Factor the following equations completely. Show work!

1.x2 – 14x - 95

2.24x2y + 6xy – 30y2

3. 5x2 - 13x + 6

Warmup 8-28Factor the following equations completely. Show work!(Check for GCF’s first)

1. 6x2 + 30x - 216

2. 4x2 - 12x + 5

3. 100 - 49x2

4. 75x2 - 27


1. 7x2 - 56x + 84

2. 3x2 - 4x - 15

3. 20x2y – 35xy2 – 45x2y2

4. 121x2 - 25


1. 2x2 + 22x - 120

2. 4x2 - 16x + 7

3. 20x2 – 45x

4. Solve the following factored equation. Show work! -2(x – 8)(3x + 4) = 0


1.4x2 - 36x + 72

2.6x2 - 5x – 4

3. 9x2 + 45x

4. 25x2 - 64


1. 4x2 - 36x + 72

2. 6x2 - 5x – 4

3. 9x2 + 45x

4. Solve the following factored equation. Show work! 3x(x + 5)(2x - 3) = 0

Warmup 9-4Solve the following equations by factoring. Show work!(Check for GCF’s first)

1.2x2 + 6x – 56 = 0

2.2x2 - 21x + 27 = 0

3. 15x2 - 9x = 0

4. 4x2 - 49 = 0

Warmup 9-8Solve the following equations by factoring. Show work!(Check for GCF’s first)

1. 3x2 - 4x - 15 = 0

2. 12x2 + 20x = 0

3. 100x2 - 81 = 0

Warmup 9-9Solve the following equations by factoring. Show work!

1. 2x2 - 22x + 48 = 0

2. 4x2 + 3x - 10 = 0

3. Solve by using the quadratic formula: 5x2 - 8x + 2 = 0


1. 4x2 + 3x - 10 = 0


3. Solve by taking the square root: 3x2 – 25 = 56

Examples – Quadratic Formula

Solve each quadratic equation below using the quadratic formula. Show work!

1. x2 + 5x - 24 = 0 2. 6x2 -17x + 12 = 0

3. 3x2 - 8x - 2 = 0 4. 5x2 + 6x - 3 = 0

5. 7x2 - 11x + 2 = 0 6. 2x2 + 9x - 3 = 0

7. x2 + 14x + 49 = 0 8. 25x2 – 60x + 36 = 0

GeometryQuadratic Formula Practice

Use the quadratic formula to solve the following quadratic equations. Show work!

1. x2 + 9x – 36 = 0 2. x2 – 7x – 44 = 0

3. x2 – 11x – 102 = 0 4. 3x2 – 10x + 8 = 0

5. 5x2 + 2x – 16 = 0 6. 27x2 – 15x + 2 = 0

7. 5x2 – 6x – 1 = 0 8. x2 + 4x – 19 = 0

9. 6x2 – 12x – 1 = 0 10. 3x2 – 6x – 4 = 0

11.3x2 + 10x - 2 = 0 12. 2x2 – 8x - 7 = 0

GeometryQuadratic Formula Practice

13. x2 – 10x + 25 = 0 14. x2 + 22x + 121 = 0

15. 9x2 – 24x + 16 = 0 16. 81x2 – 90x + 25 = 0

17.3x2 – 7x + 2 = 0 18. 2x2 – 11x + 7 = 0

19.4x2 -13x + 8 = 0 20. x2 – 6x + 25 = 0

21.4x2 - 8x + 13 = 0 22. x2 - 7x + 19 = 0

23. 5x2 -10x + 14 =0 24. 3x2 – 4x + 8 = 0

Ticket In the Door 9-9 Quadratic Formula

Solve each quadratic equation below using the quadratic formula. Show work!

1. x2 – 8x - 20 = 0

2. 2x2 + 6x – 5 = 0

3. 4x2 – 7x + 2 = 0

4. 9x2 – 48x + 64

Analytic GeometryFactoring Practice

Factor completely . Show work!1. 5x3 – 25x 2. x2 – 8x – 65

3. 4x2 – 12x + 36 4. 3x2 - 42x + 144

5. 2x2 – 36x – 126 6. 8x2 + 6x - 5

7. 12x2 – 2x – 14 8. 38x2y – 27xy2

9 2x2 – 11x + 12 10. 5x2 + 80x – 180

11. 42x3 – 35x2 12. x2 - 20x + 100

13. x2 - 15x + 54 14. 15x – 60x2

15. 4x2 + 28x + 40 16. 9x2 – 30x + 24

17. 18x2y – 9xy + 54x3y2 18. x2 - 28x + 75

19. 6x2 + 42x - 180 20. 8x4 – 12x3 – 20x2 + 48x

Ticket in the Door 8-27(Factoring)


1. x2 - 4x - 45 2. 3x2 - 14x + 8

3. 48x2y - 84xy2 4. 25x2 – 90x + 45

5. 4x2 – 16x - 128

Ticket Out the Door 9-1(Difference of Squares)


1. 49x2 - 4 2. 64x2 - 121

3. 81 - 25x2 4. 9x2 – 16

5. 50x2 - 98

Examples - Completing the Square

A = 1 Examples

Ex. x2 – 10x + 21 = 0 Ex. y2 – 14y – 51 = 0

Ex. x2 + 16x – 24 = 0 Ex. y2 + 12y - 27 = 0

Ex. x2 – 8x + 11 = 0 Ex. y2 + 18y + 68 = 0

Standard to Vertex Form Conversion Practice

For the following quadratic equations, convert each one into vertex form. Then, identify the vertex and Axis of Symmetry. Show work!

1. y = x2 – 8x + 19

2. y = -x2 - 14x - 35

3. y = -2x2 + 12x + 21

4. y = 3x2 + 30x - 56

5. y = -4x2 + 16x - 9

6. y = -x2 - 20x - 37

7. y = 5x2 -+ 40x + 63

8. y = 4x2 + 24x + 36

9. y = 2xw – 4x + 19

10. y = -3x2 – 12x

11. y = -6x2 + 24x - 11

12.y = 8x2 - 48x

Examples - Converting from standard to vertex form


1. y = x2 – 12x + 28

2. y = x2 + 4x - 3

3. y = -x2 + 10x - 22

4. y = -x2 - 8x - 11

5. y = 2x2 + 4x + 1

6. y = -3x2 + 12x - 19 7. y = 4x2 + 24x + 41

Ticket In the Door 9-10Convert from standard to vertex form


1. y = x2 – 10x + 17

2. y = -x2 + 18x - 75

3, y = 4x2 + 8x + 9

4. y = -5x2 - 30x - 32


1.x2 + 16x - 80 = 0

2.Solve by using the quadratic formula:

4x2 - 5x - 2 = 0

3.Solve by taking the square root:

6x2 + 17 = 167


1. 3x2 + 15x - 72 = 0

2. 5x2 - 14x + 8 = 0

3. Solve by using the quadratic formula: 6x2 - 7x - 3 = 0


Examples- Rate of ChangeFrom an Equation

Find the rate of change of each quadratic equation below for the given interval(x – values) Show work!

1. x2 - 4x – 6 from x = 2 to x = 4

2. x2 + 8x + 11 from x = -2 to x = -5

3. x2 - 12x + 43 from x = 3 to x = 7

4. 2x2 - 16x + 19 from x = 2 to x = 5

5. 3x2 + 12x + 5 from x = -2 to x = 0

6. 4x2 - 24x + 21 from x = 2 to x = 6

Rate of change from an equation practice

Find the rate of change of each quadratic equation below for the given interval(x – values) Show work!

1. y = x2 – 8x + 21 from x = 2 to x = 4

2. y = -x2 - 14x - 38 from x = -5 to x = -8

3. y = -2x2 + 12x – 22 from x = 1 to x = 6

4. y = 3x2 + 30x + 65 from x = -5 to x = -2

5. y = -4x2 + 16x - 9 from x = 0 to x = 3

6. y = 5x2 - 40x + 71 from x = 4 to x = 6

7. y = 4x2 + 24x + 36 from x = -6 to x = -3

8. y = 2x2 – 4x + 17 from x = -1 to x = 3

9. y = -3x2 – 12x from x = -2 to x = 2

10. y = 8x2 - 48x from x = -5 to x = -2

Ticket out the Door 9-15Rate of change from an equation

Find the rate of change of each quadratic equation below for the given interval (x – values) Show work!

1. y = x2 – 10x + 19 from x = 4 to x = 7

2. y = -2x2 - 28x – 94 from x = -7 to x = -4

3, y = 4x2 - 8x - 7 from x = 0 to x = 3

GeometryGraphing Quadratics in Standard Form with Tables Examples

Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!1. y = x2 – 4x + 9

: Vertex Form: _____________

Vertex: ________

A. O S.: ________

2. y = -x2 – 12x - 39 Vertex Form: ______________

Vertex: __________

A. O S.: ________

3. y = 2x2 + 12x + 11 Vertex Form: ______________

Vertex: __________

A. O S.: ________

X Y

X Y

X Y

GeometryGraphing Quadratics in Standard Form with Tables Examples

Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!4. y = -2x2 + 16x - 23

: Vertex Form: _____________

Vertex: ________

A. O S.: ________

5. y = 3x2 + 30x + 69 Vertex Form: ______________

Vertex: __________

A. O S.: ________

6. y = -4x2 + 56x - 188 Vertex Form: ______________

Vertex: __________

A. O S.: ________

X Y

X Y

X Y

GeometryGraphing Quadratics in Standard Form with Tables Practice

Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!1. y = -x2 – 14x - 40

Vertex Form: _____________

Vertex: ________

A. O S.: ________

2. y = 2x2 – 12x + 13 Vertex Form: ______________

Vertex: __________

A. O S.: ________

3. y = x2 - 16x + 54

Vertex Form: ______________

Vertex: __________

A. O S.: ________

X Y

X Y

X Y


Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!4. y = -2x2 – 20x - 49

: Vertex Form: _____________

Vertex: ________

A. O S.: ________

5. y = 3x2 – 12x + 5 Vertex Form: ______________

Vertex: __________

A. O S.: ________

6. y = -3x2 - 6x + 5 Vertex Form: ______________

Vertex: __________

A. O S.: ________

X Y

X Y

X Y


Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!7. y = -x2 + 8x - 13

Vertex Form: _____________

Vertex: ________

A. O S.: ________

8. y = 4x2 + 24x + 30 Vertex Form: ______________

Vertex: __________

A. O S.: ________

9. y = -4x2 + 40x - 90 Vertex Form: ______________

Vertex: __________

A. O S.: ________

X Y

X Y

X Y

GeometryGraphing Quadratics in Vertex Form with

Tables(Examples)

Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!1. y = (x - 4)2 + 3

Vertex: ________

A. O S.: ________

2. y = -(x + 3)2 - 2

Vertex: ________

A. O S.: ________

3. y = (x + 5)2 - 4

Vertex: ________

A. O S.: ________

X Y

X Y

X Y

GeometryGraphing Quadratics in Vertex Form with

Tables(Examples)

Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!4. y = 2(x + 1)2 - 6

Vertex: ________

A. O S.: ________

5. y = -2(x - 5)2 + 3

Vertex: ________

A. O S.: ________

6. y = -3(x + 7)2 + 2

Vertex: ________

A. O S.: ________

X Y

X Y

X Y

GeometryGraphing Quadratics in Vertex Form with Tables

Practice

Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!1. y = (x + 2)2 - 7

Vertex: ________

A. O S.: ________

2. y = -(x - 5)2 - 4

Vertex: ________

A. O S.: ________

3. y = (x + 3)2 + 6

Vertex: ________

A. O S.: ________

X Y

X Y

X Y


Practice

Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!4. y = 2(x - 4)2 - 9

Vertex: ________

A. O S.: ________

5. y = -2(x + 8)2 - 2

Vertex: ________

A. O S.: ________

6. y = 3(x - 1)2 - 4

Vertex: ________

A. O S.: ________

X Y

X Y

X Y


Practice

Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!7. y = -3(x + 2)2 + 5

Vertex: ________

A. O S.: ________

8. y = 4(x + 1)2 - 9

Vertex: ________

A. O S.: ________

9. y = -4(x - 3)2 + 7

Vertex: ________

A. O S.: ________

X Y

X Y

X Y

Ticket in the door 9-14Graphing quadratics from standard form

Convert each quadratic into vertex form. Identify the vertex and Axis of Symmetry for each problem. Then graph the quadratic equations by making a table of values. Show work!1. y = x2 – 6x + 7

: Vertex Form: _____________

Vertex: ________

A. O S.: ________

2. y = -2x2 + 28x - 93 Vertex Form: ______________

Vertex: __________

A. O S.: ________

3. y = 3x2 + 30x + 71 Vertex Form: ______________

Vertex: __________

A. O S.: ________

X Y

X Y

X Y

Ticket out the Door 9-10(2)Graphing Quadratics in vertex form

Identify the vertex and Axis of Then graph the quadratic equations by making a table of values. Show work!1. y = (x + 6)2 - 5

Vertex: ________

A. O S.: ________

2. y = -2(x - 3)2 + 4

Vertex: ________

A. O S.: ________

3. y = 3(x + 5)2 - 9

Vertex: ________

A. O S.: ________

X Y

X Y

X Y

Warmup 9-141.Solve by using the quadratic formula: 3x2 - 10x + 5 = 0

2. Solve by taking the square root: 8x2 - 47 = 121

3. Graph the following quadratic equation using the table provided.

x2 + 8x + 13

Vertex: __________

A.O.S. : __________

Extrema: ________

X Y

Warmup 9-151.Solve by using the quadratic formula: 4x2 - 13x - 12 = 0

2. Solve by taking the square root: 5x2 + 53 = 428

3. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. -x2 + 6x - 14

Vertex: __________ Up or down: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________ y-int: _________

X Y

Warmup 9-161. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. -x2 + 6x - 14

Vertex __________

A. O. S. : ________

Extrema: _______

2. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. 2x2 + 16x + 25

Vertex: __________ Extrema: _________A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change -6 < x < -3: _________

X Y

X Y

Warmup 9-161.Solve by using the quadratic formula: 3x2 + 11x + 4 = 0

2. Solve by taking the square root: 6x2 - 76 = 20

3. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. 2x2 + 16x + 25

Vertex: __________ Extrema: _________A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change -6 < x < -3: _________

X Y

Warmup 9-171. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -x2 - 10x - 29

Vertex: __________ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________ 2. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = 3x2 - 24x + 42

Vertex: __________ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Extrema: ________

X Y

X Y

Warmup 9-181. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -3x2 + 12x - 8


2. Find the rate of change for the graph above for: 1 < x < 4.

3. In the equation, h(t) = -9t2 + 90t + 75, a. What does the t represent?

b. What does the h(t) represent?

X Y



If we were given the graph for the equation, h(t) = -4t2 + 40t.

2. Where on the graph of this equation would we look to find the time when the maximum height occurred?

3. Where on the graph of this equation would we look to find the maximum height of the object?

4. Where on the graph of this equation would we look to find the initial height of the object?

X Y


Vertex: __________ Extrema: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change 0<x<3 : _________

For the following questions, use the equation, h(t) = -6t2 + 36t + 76.

2. Find the height of the object at 5 seconds, or h(5).

3. What is the initial height of the object?

4. At what time did the object reach its maximum height?

5. What was the maximum height of the object?

X Y

Warmup 9-301. Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -x2 - 14x -43

Vertex: __________ Extrema: _______ A. O. S. : __________ Interval of Increase: ________ Domain: ___________ Interval of Decrease: ________ Range: ____________ Rate of Change -7<x<-5 : _________

For the following questions, use the equation, h(t) = -3t2 + 24t.





6. For what time interval was the object going down?

X Y

Warmup 10-1For the following questions, use the equation, h(t) = -5t2 + 30t + 35.





5. For what time interval was the object going up?

6. Complete the square for the following equation: x2 – 14x + 33 = 0

7. Complete the square for the following equation: y2 + 20y - 44 = 0

Warmup 10-2

For 1-2, write an equation of a circle in standard form for the given information.

1. Center = (7, 0) and r = 43

2. Center = (8, -3) and r = 13

For the following circle equations, identify the center and radius.

3. (x - 7)2 + (y + 3)2 = 81

4. Solve by completing the square. Show work! x2 + 16x - 26 = 0

GeometryStandard Form Analysis

1. Vertex: __________ Up or down: _______ A. O. S. : __________ Domain: ___________ Range: ____________ y-int: _________




5. Vertex: __________ Up or down: _______ A. O. S. : __________ Domain: ___________ Range: ____________ 7. Vertex: _______ y-int: _________ A.O.S. : _______ Domain: ________6. Vertex: __________ Up or down: _______ Range: ________ A. O. S. : __________ Y-int: ________ Domain: ___________ Up or Down: _______ Range: ____________ y-int: _________





12. Vertex: __________ Up or down: _______ A. O. S. : __________ Domain: ___________ Range: ____________ 14. Vertex: _______ y-int: _________ A.O.S. : _______ Domain: ________13. Vertex: __________ Up or down: _______ Range: ________ A. O. S. : __________ Y-int: ________ Domain: ___________ Up or Down: _______ Range: ____________ y-int: _________

Notes - Quadratic Applications

Basic Equation Terms: h(t) = -at2 + bt + c1. t = time in seconds2. h(t) = height of object at t seconds.

Questions about graphs of quadratic applications.

What part of a quadratic graph represents:

3. The height of the object at a given time?

2. The initial height of the object when it is thrown/launched?

3. The time when the object reaches its maximum height?

4. The maximum height of the object?

5. The time when the object hits the ground?

6. The total time the object is in the air?

Questions about dealing with a quadratic application equation.

7. How do we find the height of the object at a given time?

2. How do we find the time the object reaches its maximum height?

3. How do we find the maximum height of the object?

4. Where in the equation can we find the initial height of the object?

Ticket out the door 9-16

For the following questions, use the graph from the equation, h(t) = -3t2 + 36t. (on the back of one of the graphs used in the notes)

1. What is the height of the object at 9 seconds or h(9)?




5. When did the object land on the ground?

6. How long was the object in the air?

For the following questions, use the equation, h(t) = -4t2 +48t + 56






For the following questions, use the graph from the equation, h(t) = -5t2 + 30t + 55. (on the back of one of the graphs used in the notes)





For the following questions, use the equation, h(t) = -2t2 +32t





Warmup 9-29






For the following questions, use the equation, h(t) = -3t2 + 54t + 27





Mini Quiz Quadratic Applications

For the following questions, use the graph from the equation, h(t) = -5t2 + 60t + 15.






For the following questions, use the graph of the equation, h(t) = -3t2 + 24t





10. When did the object hit the ground?

11. For what time interval was the object going down?

Mini Quiz Quadratic Applications

For the following questions, use the equation, h(t) = -4t2 + 64t.






For the following questions, use the graph of the equation, h(t) = -7t2 + 42t + 57







For the following questions, use the equation, h(t) = -4t2 +48t + 56





5. In what time interval would the object be going up?

Quadratic Application Practice

For the following questions, use the graph from the equation, h(t) = -2t2 + 20t.














Quadratic Application Practice

For the following questions, use the equation, h(t) = -3t2 + 54t










Quadratic Application Review

For the following questions, use the graph from the equation, h(t) = -6t2 + 60t.












11. When did the object land on the ground?(Approximately)

12. How long was the object in the air? Approximately)

Quadratic Application Review

For the following questions, use the equation, h(t) = -4t2 + 48t










Examples – Completing the Square

A = 1 Examples

Ex. x2 – 10x + 18 = 0

Ex. x2 + 16x – 24 = 0

Ex. y2 – 8y – 12 = 0

Ex. y2 + 2y + 9 = 0

Ticket out the Door 9-30

Complete the square in each problem below. Show work!

1. x2 – 18x + 45 = 0

2. y2 + 8x – 56 = 0

3. y2 – 6y + 18 = 0

4. x2 + 4x - 9 = 0

Completing the Square Practice


1. x2 + 4x - 12 = 0 2. x2 – 10x - 56 = 0

3. x2 - 22x + 84 = 0 4. y2 + 16x – 60 = 0

5. y2 – 28y + 150 = 0 6. y2 - 24y – 96 = 0

7. x2 + 12x - 108 = 0 8. x2 – 12x + 15 = 0

9. x2 + 6x - 13 = 0 10. y2 – 2y + 11 = 0

Examples – Circles in Standard Form Part 1

Standard Form for a Circle Equation:

(x - h)2 + (y – k)2 = r2

center of circle is (h, k) (opposite of each number in parenthesis) r = radius of circle (must take square root of r2 to get r )

Writing the equation of a circle in standard form given the center and radius.

Ex. Center = (2.-3) , radius = 6

Ex. Center = (-4, 0), radius = 3

Ex. Center = (7, 8), radius = 10 (remember, squaring a square root cancels it out)

Ex. Center = (5, -1), radius = 23

Given the equation in standard form, identify the center, radius and diameter.

Ex. x2 + y2 = 144 Ex. x2 + (y – 2)2 = 36

Ex. (x + 4)2 + y2 = 81 Ex. (x – 6)2 + (y + 3)2 = 25

Ex. (x + 1)2 + (y – 9)2 = 121

Examples – Circles in Standard Form Part 2

Standard Form for a Circle Equation:

(x - h)2 + (y – k)2 = r2

center of circle is (h, k) (opposite of each number in parenthesis)

Use completing the square to write a circle equation in standard form. Then identify the center, radius, and diameter of the circle:

Ex. x2 -12x + y2 -13 = 0 Ex . x2 + y2 + 8y – 105 = 0

Ex. x2 + 10x + y2 – 39 = 0 Ex. x2 + y2 – 6y - 72 = 0

Ticket in the door 10-2

Write the equation of a circle in standard form for the given information.Show work!

1. Center = (-2-5), r = 7

2 Center = (0, -8), r = 35

For the following circle equations written in standard form, identify the center, and radius.

3. (x + 7)2 + y2 = 25

4. (x – 3)2 + (y + 4)2 = 196


5. x2 – 18x + 45 = 0 6. y2 + 8x – 56 = 0


For #1- 2, use completing the square to write the circle equation in standard form. THEN, LIST the Center, and Radius. Show work!

1. x2 + y2 – 18y – 88 = 0

2. x2 – 12x + y2 – 45 = 0

Warmup 10-6

For #1 below, write an equation of a circle in standard form for the given information.

1. Center = (7, -12) and r = 36

2. Complete the square in the problem below. Show work! y2 - 14y - 5 = 0

For the following circle equations, identify the center and radius.(Complete the square in 4 and 5 first.) 3. (x – 9)2 + y2 = 225

4. x2 + 16x - 132 + y2 = 0

5. (x + 3)2 + y2 - 6x - 112 = 0

GeometryMini Quiz

Completing the Square and Circles in standard form


1. Center = (-5, 4) and r = 52 2. Center = (0, -6) and r = 8

Complete the square in the problems below. Show work!3. x2 + 22x + 41 = 0 4. y2 – 14y - 95 = 0

For the following circle equations, identify the center and radius.(Complete the square if needed first) 5. x2 + (y + 7)2 = 169 6. (x – 5)2 + (y + 9)2 = 256

7. (x + 6)2 + y2 - 20y - 44 = 0 8. x2 + 20x + 19 + y2 = 0

Warmup 10-8


1. Center = (4, -5) and r = 16


2. (x – 8)2 + y2 - 10x – 171 = 0

3. Find the distance and midpoint for the following pair of points. Show work!

(-5, 2) and (3, -4)

4. Find the slope of the following two points. Show work! (-3, 7)(11, -1)

Warmup 10-7


1. Center = (0, -9) and r = 21

2. Center = (-5, 7) and r = 8


3. (x + 3)2 + (y – 11)2 = 49

4. x2 + 14x - 32 + (y + 6)2 = 0 5. x2 + y2 – 12y + 27 = 0

Warmup 10-9


(-6, -5) and (-10, 2)


3. Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!)

A(2.-1) B(4, 2) C(7, -4) D(9, -1)

Warmup 10-12


(4, 1) and (-11, 9)



A(-3.5) B(1, -1) C(-2, -3) D(-6, 3)

Warmup 10-15


(-4, -7) and (2, -10)

2. Find the slope of the following two points. Show work! (5, 9)(-4, 30)

3. Find the area and circumference of a circle with a diameter = 30cm.

4. Find the volume of a cylinder with a diameter = 12m and a height of 7m.

5. Find the volume of a cone with a radius = 15mm and a height of 9mm.

Warmup 10-15

For #1-4, use the volume of a cone or cylinder formula to help solve each problem. Show work!

1. How many cubic feet of water would fit in a cylindrical pool that has a diameter of 24ft and a height of 6ft?

2. How many cubic inches of ice cream would fit in a cone that has a radius of 4 inches and a height of 10 inches?

3. A person has two cans of soup. The first can has a radius of 8cm, and a height of 14cm. The second can has a diameter of 20cm, and a height of 9cm. Which can has more soup in it?

4. A company currently produces a cone shaped paper cup with a diameter of 4 inches and a height of 5 inches. They are looking into making a new design which will have a radius of 3 inches and a height of 6 inches. How much more water will fit into the newer version?

Warmup 10-16

1. In a subdivision, all of the lots are arranged as quadrilaterals. Lot 1 has dimensions of 60ft, 90ft, 75ft, and 105ft. Lot 2 has dimensions of 96ft, 168ft, 120ft, and 144ft. Do these two lots for similar polygons? Show why or why not.

2. In a subdivision, all of the lots are arranged as quadrilaterals. Lots 3 and 4 are similarly shaped. Lot 3 has dimensions of 96ft, 160ft, 196ft, and 128ft. Lot 4 has dimensions of 108ft, 81ft, 162ft, and 135ft. What would the scale factor be from Lot 4 to Lot 3?

3. In a subdivision, 2 neighbors want to have rectangular in-ground pools put in. Neighbor 1 plans to have their pool be 42ft long and 18ft wide. Neighbor 2 knows that their pool will need to be 35ft long. How wide should neighbor 2’s pool be to make the two pools similarly shaped?

4. Instant oats come in packages that are cylinder shaped. A store sells two sizes of these oats. The smaller package has a diameter of 8in and a height of 15in. The larger package has a radius of 6in and a height of 20in. How many more cubic inches of oats are in the larger cylinder?

Warmup 10-28

1. If a cedar chest has a base that is 54 inches by 27 inches, and is 20 inches tall, how many cubic inches of storage space does it have?

2. A roof is 24 feet across the base, and is 14 feet high. If the roof is 45 feet long, what is the storage space of the attic inside the roof?

3. A box of Oxy-Clean is 25cm by 25cm by 42cm. How many cubic centimeters of detergent can the box hold?

4. Two neighbors are having in-ground pools installed at their homes. Neighbor 1 plans to have a pool that is 45ft long by 20ft wide, by 10ft deep. Neighbor 2 wants their pool to be 42ft long by 24ft wide, by 9ft deep. Which neighbor’s pool will hold more water?

5. The company who makes tootsie rolls is considering changing their packaging from a cylinder to a triangular prism. Their current packaging has a diameter of 4 inches and a height of 16 inches. The new design has a base that is 6 inches, and a height of 5 inches. If the height of the prism is still 16 inches, how many more cubic inches of tootsie rolls will fit in the new package design? (must get a decimal from multiplying by pi in the cylinder volume)

Mini Quiz Midpoint, Distance, Slope, Area, Circumference

and Volume Formulas


(-3, 7 ) and (-10, -17)

2. Find the slope of the following two points. Show work! (-8, 5)(-24, -9)


E(4, 7) F(7, 3) G(4, -1) H(1, 3)

Mini Quiz Midpoint, Distance, Slope, Area, Circumference

and Volume Formulas

4. Find the area of a circle with a diameter = 26in. Show work!

5. Find the circumference of a circle with a radius = 17ft. Show work!

6. Find the volume of a cylinder with a radius = 18m, and a height = 12m. Show work!

7. Find the volume of a cone with a diameter = 42cm, and a height = 15cm. Show work!

Special Quadrilateral Coordinate Geometry Practice

Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!)

1. A(-5, 4) B(-2, 6) C(2, 0) D(-1, -2)

2. E(-8,5) F(1. -2) G(-5,-6) H(4, -13)

3. I(1, 4) J(5,5) K(3, -4) L(7, -3)

4. M(-6, 2) N(-3, 0) P(-1, 3) Q(-4, 5)

5. R(-5, -1) S(-4, 6) T(0, 4) U(1, 11)

6. V(4,4) W(0, -2) X(-6, 2) Y(-2, 8)

7. Z(-2, 5) A(2, 8) B(4.-3) C(8, 0) 8. D(0, 5) E(-2, 14) F(4, 7) G(6, -2)

Ticket in the Door 10-9Special Quadrilaterals Coordinate Geometry

Use the slope, distance, or midpoint formula with the following set of 4 points to determine whether they represent a rhombus, rectangle, or square.(must show they make a parallelogram first!)

1. A(-2, 3) B(2, 6) C(7, 6) D(3, 3)

2. E(1, 1) F(5. 3) G(4, 5) H(0, 3)

Warmup 10-8


E(-6.-2) F(-4, -5) G(-6, -8) H(-8, -5)

2. Find the area of circle with a radius = 14(leave answer in terms of pi.)

3. Find the circumference of a circle with a radius = 17.(leave answer in terms of pi.)

Circles in Standard Form Practice

Write the equation of a circle in standard form for the given information.

1. Center = (0,0) , r = 12 2. Center = (0, 0), r = 2 7

3 . Center = (2, -5), r = 15 4. Center = (-4, 3), r = 62

5. Center = (0, -8), r = 11 6. Center = (9, 0), r = 45

7. Center = (-12, -5), r = 18 8. Center = (7, 10), r = 1.5

For #9-14, use completing the square to write the circle equation in standard form. THEN, LIST the Center, Radius, and Diameter. Show work!

9. x2 - 4x + y2 = 21 10. x2 + y2 + 16y = 36

11.4x2 + 4y2 – 40y = 224 12. 9x2 + 54x + 9y2 = 63

13. 7x2 – 14x + 7y2 + 56x = 133 14. 6x2 + 48x + 6y2 – 24x = 606

Circles in Standard Form Practice(Part 2)

In the following problems, use completing the square to write the circle equation in standard form. THEN, LIST the Center, Radius, and Diameter. Show work!

1. x2 - 4x + y2 – 21 = 0 2. x2 + y2 + 16y – 36 = 0

3. x2 + y2 – 10y - 56 = 0 4. x2 + 6x + y2 - 7 = 0

5. x2 - 26x + y2 + 105 = 0 6. x2 + y2 + 28y + 96 = 0

7. x2 – 2x - 35 + (y + 4)2 = 0 8. (x - 6)2 + y2 – 16y - 161 = 0

9. (x + 5)2 + y2 – 14y + 13 = 0 10. x2 - 20x – 96 + (y – 9)2 = 0

11. (x – 12)2 + y2 + 4y - 5 = 0 12. x2 - 22x + 117 + (y + 3)2 = 0

Circles in Standard Form Practice(1)


1. Center = (0,0) , r = 19 2. Center = (0, 0), r = 210

3 . Center = (0, -7), r = 24 4. Center = (5, 0), r = 37

5. Center = (-1, -4), r = 21 6. Center = (3, -6), r = 47

7. Center = (11, 3), r = 27 8. Center = (-9, 2), r = 3.5

9. Center = (10, -12), d = 14 10. Center = (3, 5), d = 32

11.Center = (0, -6), d = 30 12. Center = (-13, 0) , d = 8

For #13-18, identify the center, radius, and diameter of each circle.

13. (x – 8)2 + y2 = 81 14. x2 + y2 = 289

15. (x - 2)2 + (y + 4)2 = 225 16. (x + 1)2 + (y + 7)2 = 484

17. (x - 5)2 + (y - 12)2 = 4 18. (x + 3)2 + (y – 9)2 = 42

Circles in Standard Form Practice


1. Center = (0,0) , r = 12 2. Center = (0, 0), r = 2 7

3 . Center = (2, -5), r = 15 4. Center = (-4, 3), r = 62

5. Center = (0, -8), r = 11 6. Center = (9, 0), r = 45

7. Center = (-12, -5), r = 18 8. Center = (7, 10), r = 1.5

9. Center = (-8, 0), d = 14. 10. Center = (6, -7), d = 22

11.Center = (0, 12), d = 34 12. Center = (-9, -2) , d = 18

For #13-18, identify the center, radius, and diameter of each circle.

13. x2 + (y + 4)2 = 49 14. (x – 5)2 + y2 = 100

15. (x + 7)2 + (y – 1) 2 = 196 16. (x – 9)2 + (y + 6)2 = 121

17. (x + 4)2 + (y + 10)2 = 1 18. (x – 2)2 + (y – 8)2 = 10

Parallel Lines cut by a Transversal Practice

For the following problems, name 1 pair of angles in the picture at the right that fits each type listed below.1. Alternate exterior 2. Same Side Interior

3. Vertical Angles 4. Alternate Interior

5. Corresponding 6. Supplementary

In the figure, Line L is parallel to Line M. For #7-14, tell what type of angles each pair listed is AND tell whether the angles are congruent(=) or supplementary(add to = 180). 7. <2, <5 8. <7, <3

9. <3,<6 10. <2, <7

11. <1, <4 12. <6, <8

13. <4, <7 14. <7, <8

For #15-20, use the figure at the right. LineL is parallel to Line M. If < 4 = 73, find the measure of each angle below and identify the type of angle each forms with <4.

15. <7 16. < 1

17. <5 18. <2

19. <8 20. Using the measure of <8 from #13, find the measure of <3 and give the type of angle.

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Parallel Lines cut by a Transversal Extra Practice

For the following problems, name 1 pair of angles in the picture at the right that fits each type listed below.1. Alternate exterior 2. Same Side Interior

3. Vertical Angles 4. Alternate Interior

5. Corresponding 6. Supplementary

In the figure, Line L is parallel to Line M. For #7-14, tell what type of angles each pair listed is AND tell whether the angles are congruent(=) or supplementary(add to = 180). 7. <2, <5 8. <6, <3

9. <3,<2 10. <2, <7

11. <8, <4 12. <7, <8

13. <3, <7 14. <2, <1

For #15-20, use the figure at the right. LineL is parallel to Line M. If < 4 = 58, find the measure of each angle below and identify the type of angle each forms with <4.

15. <7 16. < 1

17. <5 18. <2

19. <8 20. Using the measure of <7 from #13, find the measure of <3 and give the type of angle.

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In the picture at the right, line L is parallel to line M. Name the type of angles given in each problem below.

1. <5, <72. <2, < 83. <2, <34. <4, <65. <1, <76. <3, <5

In the picture at the right, Line L is parallel to Line MIf <5 = 132, find the measure of the following angles. THEN, describe the type of angle each one forms with <5.

7. <78. <89. <410. <111. <2

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Parallel Lines cut by a Transversal Practice(part 2)

7. If <8 = 14x – 72, and <4 = 5x – 18, solve for x.

8. If <1 = 12x + 45, and <7 = 6x – 9, solve for x.

9. If <5 = 19x - 33, and <7 = 5x + 65, solve for x.

10 . If <6 = 8x + 73, and <4 = 21x – 44, solve for x.


12. If <8 = 17x - 23, and <6 = 25x – 119, solve for x.

13. If <3 = 10x + 51, and <6 = 4x – 25, solve for x.

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For the following problems, use the figure at the right. In the figure, Line L is parallelto Line M. Show work on all problems!

1. If <1 = 16x – 49, and <6 = 3x + 29, solve for x. 2. If <6 = 7x - 53, and <7 = 5x – 31, solve for x.

3. If <2 = 9x + 61, and <4 = 3x + 102, solve for x.


5. If <2 = 14x - 37 , and <5 = 5x - 1, solvefor x.

6. If <8 = 19x + 46, and <1 = 31x - 50, solve for x.

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Examples – Parallel Lines cut by a Transversal

(Part 2)

1. If line L is parallel to line M at the right, <3 = 12x – 42 and <1 = 7x + 23, solve for x.

2. If line L is parallel to lineM at the right, <2 = 4x + 53, <4 = 11x - 8, solve for x.

3. If line L is parallel to line M at the right, < 5 = 21x + 73, and <7 = 5x + 121, solve for x.

4. If line L is parallel to line M, <1 = 15x - 59, and <8 = 19x - 103, solve for x.

5. If line L is parallel to line M, <6 = 11x + 82, and <2 = 18x - 16, solve for x.


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1. If line L is parallel to line M at the right, <8 = 11x – 31 and <4 = 7x + 25, solve for x.

2. If line L is parallel to lineM at the right, <2 = 6x – 41, <6 = 4x -29, solve for x.

3. If line L is parallel to line M at the right, < 7 = 13x + 63, and <3 = 19x + 15, solve for x.


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Warmup 10-21

In the picture at the right, line L is parallel to line M. Name the type of angles given in each problem below. THEN, tell whether each pair is = or add to = 180.

1. <8, <42. <2, <83. <6, <74. <7, <25. <1, <86. <3, <4

In the picture at the right, Line L is parallel to Line M. If <3 = 141, find the measure of the following angles. Give a reason(type) for each answer.

7. <88. <79. <110. <411.What would <2 =?(compare it to <4 found in #10.)

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Warmup 8-17(Geom) Add or subtract each set of polynomials. Answers should be in standard form. Show...

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Transcript of Warmup 8-17(Geom) Add or subtract each set of polynomials. Answers should be in standard form. Show...