REVIEW FOR QUIZ! NAME: __________________________ DUE TUES/WED Solve each equation (use the method provided) 1. Square Roots Method (x + 3)2 + 2 = –10

2. Factor to solve. x2 – 2x – 15 = 0

3. Complete the Square. x2 – 8x + 3 = 0

4. Quadratic Formula. 6x2 + 2x + 1= 0

Solve each equation. 5. y = 2 (x – 3)2 + 8 (square roots) 6. y = 2x2 + x – 10 (factor and zero prod)

7. y = x2 – 14x + 1 (complete the square) 8. y = x2 – 2x + 5 (quadratic formula)

SOLVING: WHICH METHOD SHOULD YOU USE? Explain why!

Equation A B C D

1 x2 + 4x + 3 = 0 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

2 5x2 – 1 = 6 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

3 x2 – 7x + 1 = 0 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

4 x2 + 10x + 4 = 0 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

5 x2 – 14x = 5 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

6 5 – 3x2 = 20 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

7 x2 + x = 10 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

8 x2 – 4x – 12 = 0 Sq. Roots Factor/ZPP Complete Sq. Quad. Form

Solve: Choose which method is best =) 1. y = 2 (x + 2)2 + 24 2. y = x2 – 6x + 8

3. y = 2x 2 −5x −12 4. y = x2 – 12x + 1

Find the discriminant and determine the number and type of solutions. Discriminant Number and Type of Solutions

5. y = 3x2 – 3x + 2

6. y = x2 – 10x + 1

7. y = x2 – 4x + 4

REVIEW PACKET SECTION 1: FACTORING Factor Completely! 1. x2–7x+6 2. x2–100

3. 4x2+81 4. 25p2–16p

5. m2–10m+21 6. y2–3y–18

7. x2+7x+12 8. 4x2+20x–24

9. 4x2+20x+25 10. 16a2–49b2

11. 16x2+6x 12. x2–2x+1

13. 16a2–81 14. 3x2+3x–36

15. x2–8x+16 16. 24z2–14z–5

17. 3m2–7m+2 18. 3x2–75

SECTION 2: SOLVING Usethesquarerootmethod.1. 5x2–7=60 2. x2+16=0

3. 5x2+9=134 4. 2(x+3)2+12=4

Factorandusethezeroproductproperty.5. (2x+8)(x–5)=0 6. x2–2x+1=0

7. x2+6x=0 8. 6x2+11x=10

CompletetheSquare.9. x2–4x–12=0 10. x2–2x–35=0

11. x2+6x=23 12. 4x2–8x=40

UsetheQuadraticFormula.13. x2+5x–6=0 14. 2x2–4x+3=0

15. 2x2–x–4=2 16. 10x2+9=x

SECTION 3: GRAPHING

Find the vertex of each quadratic function: 1. f(x) = (x+ 2)2 + 5

( , ) 2. f(x) = –2x2 – 3

( , )

3. f(x) = (x – 1)2 ( , )

4. f(x) = 5x2 ( , )

5. f(x) = (x + 10) (x – 2)

( , )

6. f(x) = x2 + 2x + 5

( , )

7. f(x) = 2 (x – 5) (x + 3)

( , )

8. f(x) = 2x2 + 8x + 5

( , )

9.y=–3 (x – 1)2 + 10 OpensUporOpensDown Stretched,Shrink,Standard10. y=(x + 4)2 + 4 OpensUporOpensDown Stretched,Shrink,Standard 11. Name 3 synonyms for “solution”: _______________, _______________, _______________ Graph.

12. y = 2 x +5( )2 −3

13. y =−1

2 x +5( ) x −3( ) 14. y = x 2 +4x −6

Quick Questions. Choose either ANSWER A or ANSWER B. QUESTION ANSWER A ANSWER B

1 What is the form of the function: y = 2x2 + 3x + 2

Intercept Form Standard Form

2 What is the form of the function: y = 2(x + 3)2 – 10 Vertex Form Intercept Form

3 What is the form of the function: y = – (x + 3) (x – 8) Intercept Form Standard Form

4 What formula will find the x-coordinate of the vertex for standard form?

x = −b2a

x = b

2⎛⎝⎜

⎞⎠⎟

2

5 What formula will find the x-coordinate of the vertex for intercept form?

x = p − q2

x = p + q

2

6 What is the value of C that would complete the square: x2 – 4x + C 4 16

7 What is the a-value: y = 2x2 + 5x + 2 1 2

8 What type of polynomial is always prime?

A binomial sum of squares A trinomial

9 What method would you use to solve the equation: y = (x + 3) (2x + 1)

Zero Product Property Complete the Square

10 What method would you use to solve the equation: y = 4x2 + 10

Square Roots Method Quadratic Formula

11 What method would you use to solve the equation: y = x2 + 10x + 3

Square Roots Method Complete the Square

12 The discriminant is 24. How many solutions are there?

2 1

13 The discriminant is -10. How many solutions are there?

0 2

14 The discriminant is 0. How many solutions are there? 1 0

15 The discriminant is -25. What type of solutions are there? Real Imaginary

16 The discriminant is 4. What type of solutions are there? Real Imaginary

17 How do you find any x-intercept? Substitute 0 for x Substitute 0 for y

18 How do you find any y-intercept? Substitute 0 for x Substitute 0 for y

19 What is the quadratic formula? x = −b b2 − 4ac

2a

x =

−b ± b2 − 4ac2a

20 What calculator function can you use to find the vertex of a parabola? 2nd Graph 2nd TRACE

WHAT SHOULD YOU DO NEXT? (when solving with square roots or factoring methods)

1. 2x2 + 8 = 10 A. Divide both sides by 2. B. Isolate x2. C. Square root both sides.

2. (x + 4)2 = 25 A. Distribute the square. B. FOIL. C. Square root both sides.

3. x2 – 25x = 0 A. Factor into (x + 5) (x – 5). B. Add 25x to both sides. C. Factor out x.

4. x2 + 5x + 4 = 0 A. Square root both sides. B. Subtract 4 from both sides. C. Factor the trinomial.

5. x2 + 3x = 10 A. Square root both sides. B. Subtract 3x from both sides. C. Subtract 10 from both sides.

6. (3x + 1) (x + 4) = 0 A. Set each factor equal to 0. B. FOIL. C. Combine like terms.

WHAT SHOULD YOU DO NEXT in order to factor?7. 2x2 + 7x + 3 A. List pairs of factors of 3. B. Multiply 2 and 3. C. Factor out x.

8. 9x2 – 30x + 25

A. Try (3x – 5)2 and check it.

B. Multiply 9 and 25.

C. Set it equal to 0 and solve.

WRITE THE NEXT STEP ONLY! 1. (x + 5)2 = –49 2. x2 – 9x = 0

3. 2x2 + 4 = 8 4. 4x2 – 81 = 0

5. x – 2 = ± 3 6. x + 1 = ±6i

7. Complete the square. x2 – 6x + 10 = 0

8. Complete the square. x2 + 8x = 3

9. Complete the square. x2 + 10x + 25 = 6

10. Quadratic Formula. x2 + 8x = 3

11. Quadratic Formula.

x =

2 ± 9− 2(−2)(−4)

4

12. Quadratic Formula.

x = −10 ± 6i 2

4

Unit 4 QUADRATICS Summary Sheet SECTION 1: FACTORING

1. Put the polynomial in order of decreasing degree (standard form).

10 + 7x + x2 All Types

2. Factor out the GCF (include any variables!) 4x2 + 14x

Binomial A2 – B2

If it is a difference of squares, factor into conjugates. Formula: ___________________________________

x2 – 100

Binomial A2 + B2

If it is a sum of squares, the binomial is PRIME. x2 + 100

Trinomial x2 + Bx + C

If A = 1, 1. List the pairs of factors of C. 2. Find a pair that has a sum/difference of the target #. 3. Write the two binomials.

x2 + 7x + 12

Trinomial

x2 + Bx + C

If A = 1, 1. Multiply A and C and list pairs of factors. 2. Find a pair that has a sum/difference of the target #. 3. Factor by grouping.

(or factor by trial and error)

2x2 – 3x – 20

Perfect Square

Trinomial

1. If the first and last terms are perfect squares: 2. Try writing it as a binomial squared. 3. CHECK that the middle term works!!

4x2 + 28x + 49

SECTION 2: GRAPHING A quadratic function is a function with 2 as the highest degree (exponent)

Vertex Form Intercept Form Standard Form

y = a x − h( )2 +k

Vertex: (h, k) 1. a > 0: opens up a < 0: opens down 2. a < -1 or a > 1: stretched -1 < a < 1: compressed 3. Use the squares chart to find other points on the graph.

y = a(x − p)(x − q )

Vertex:

p + q

2, f

p + q

2( ) ⎛

⎝⎜⎞⎠⎟

1. Find the x-coordinate of the vertex. 2. Substitute it into the function to find the y-coordinate of the vertex. 3. Use the chart to find other points on the graph.

y = ax 2 + bx + c

Vertex:

−b2a

, f−b

2a( ) ⎛

⎝⎜⎞⎠⎟

1. Find the x-coordinate of the vertex. 2. Substitute it into the function to find the y-coordinate of the vertex. 3. Use the chart to find other points on the graph.

SECTION 3: SOLVING 1. Square Roots. Use When: An equation has an x2 or (x + c)2 (but does not have an x) 1. Isolate the x2. 2. Square root both sides. 3. Simplify (including the square root!) 4. Don’t forget the ± sign!

2. Factor and Zero Product Property. Use When: The equation is factorable. 1. Make sure the equation is in the form: ax2 + bx + c = 0 2. Factor completely! 3. Set each factor equal to 0. 4. Solve. 5. Write the solutions together: x = ____, ____

3. Complete the Square. Use When: The trinomial is not factorable. A=1 and B is even. 1. Make sure the equation is in the form: Ax2 + Bx = C

2. Use the formula

B2

⎛⎝⎜

⎞⎠⎟

2

to determine C.

3. Add C to both sides. 4. Factor the left side of the equation into a binomial squared. 5. Take the square root of both sides (don’t forget ± ) 6. Isolate the x.

4. Quadratic Formula. Use When: The other methods do not apply. 1. Put the equation into standard form: Ax2 + Bx + C = 0 2. Find A, B, C. 3. Substitute A, B, and C into the quadratic formula. Use parentheses! 4. Simplify completely!

Quadratic Formula: x =

−b ± b2 − 4ac2a

Discriminant : b2 – 4ac If negative = 2 imaginary solutions If 0 = one real number solution If positive = 2 real number solutions

Recall, i = −1

Quadratic Equations Methods Name: _______________________________________________ Period: ________ I. What makes an equation a quadratic equation? II. There are four methods. List them! A. B. C. D. III. How can you determine which method to use?

A. USE SQUARE ROOTS METHOD IF: If the equation has ______________________ OR ______________________ , (and no ____________)

B. FACTOR AND USE THE ZERO PRODUCT PROPERTY IF: If the equation has ______________________ AND ______________________ , IF THE FIRST TWO METHODS DON’T WORK, CHOOSE BETWEEN THESE TWO:

C. COMPLETE THE SQUARE IF: A = 1 AND the middle term is _________________.

D. USE THE QUADRATIC FORMULA IF: The middle term is _________________.

1. x2 + 6x + 5 = 0

2. 4(x+2)2 + 100 = 14

3. x2 – 49 = 0

4. x2 + 8x + 1 = 10

5. -2 = 2x2 + 8

6. x2 + 3x + 1 = 0

7. 4x2 + 12x + 9 = 0

8. x2 + 6x + 3 = 0

9. x2 – 36x = 0

10. x2 + 100 = 0

11. x2 + 8x + 16 = 3

12. x2 + 11x = 4

1. x2 + 6x + 5 = 0

Factor/ZPP

2. 4(x+2)2 + 100 = 14

Sq. Roots Method

3. x2 – 49 = 0

Factor/ZPP

4. x2 + 8x + 1 = 10

Complete the Square

5. -2 = 2x2 + 8

Sq. Roots Method

6. x2 + 3x + 1 = 0

Quadratic Formula

7. 4x2 + 12x + 9 = 0

Factor/ZPP

8. x2 + 6x + 3 = 0

Complete the Square

9. x2 – 36x = 0

Factor/ZPP

10. x2 + 100 = 0

Sq. Roots Method

11. x2 + 8x + 16 = 3

Complete the Square

12. x2 + 11x = 4

Quadratic Formula

QUADRATIC EQUATIONS SORT MAT

Sq. Roots Method

Factor/Zero Product Property

Complete the Square

Quadratic Formula

QUADRATIC EQUATIONS SORT MAT

Sq. Roots Method

2, 5, 10

Factor/Zero Product Property

1, 3, 7, 9

Complete the Square

4, 8, 11

Quadratic Formula

6, 12