Algebra 1 Packets 4/14-5/1 -- Mrs. Tackett

Algebra 1 Packets 4/14-5/1 -- Mrs. Tackett

● If you can access Google Classroom, there are videos I made explaining, step by step,

the notes that are attached. You can access on a laptop, or download the Google

Classroom app on your phone/tablet.

○ Here are the codes if needed:

■ Period 1-2: a25yohy

■ Period 3-4: f5bothx

■ Period 6-7: wvpcfhv

● The schedule for April 14-May 1

○ 4/14: Have 8.6 SGI completed (sent in previous packet)

○ 4/15-4/16: 8.7 notes & 8.7 SGI (Evens, front and back) (sent in previous

packet)

○ 4/17: Nothing -- Make sure you are completed with Chapter 8.

○ 4/20-4/21: 9.1 Notes and 9.1 Practice

○ 4/22-4/23: 9.2 Notes and 9.2 Skills Practice

○ 4/24: Email Mrs. Tackett pictures of completed 9.1-9.2 work

○ 4/27-4/28: 9.3 Notes and 9.3 Practice

○ 4/29-4/30: 9.4 Notes and 9.4 SGI (Evens, front and back)

○ 5/1: Email Mrs. Tackett pictures of complete 9.3-9.4 work

● If you have internet access, complete 10 ALEKS topics each week to help boost your

grade.

● Mrs. Tackett’s Contact Info: [email protected]

● A graphing calculator will be helpful (but it can be done without one)

○ Desmos

■ You can go online to desmos.com/calculator

■ You can download the desmos graphing calculator app through the

app store on your phone/tablet for free

mailto:[email protected]

9.1 Characteristics and Graphing Quadratics Notes COMPLETED

1

9.1

a) Characteristics of Quadratic Functions

b) Graphing Quadratic Functions

Use this lesson to complete 9.1 Practice

April 20, 2020


2

Characteristics of QuadraticsParabola

Standard Form

Vertex

Axis of Symmetry

Maximum

Minimum

The shape that a quadratic functions makes

The line that cuts the parabola in half

The point the axis of symmetry goes throughWhere the parabola turns

The lowest point on the graph

The highest point on the graph

If a>0, graph has a minimum

If a<0, graph has a maximum

Using standard form

Axis of Symmetry:

y-intercept:


3

Identify Characteristics from a Given Graph


4

Identify Characteristics from a Given Function


5

Maximum and Minimum Values


6

Maximum and Minimum Values


7

Application


8

How to Graph a Quadratic by Hand

**Only do this if you DO NOT have a graphing calculator or access to Desmos

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 9 8 Glencoe Algebra 1

9-1 Practice Graphing Quadratic Functions

Use desmos to graph each function. Determine the domain and range.

1. y = –𝑥2 + 2 2. y = –2𝑥2 – 8x – 5

Find the vertex, the equation of the axis of symmetry, and the y–intercept of the graph of each function.

3. y = –2𝑥2 + 8x – 5

Consider each equation. Determine whether the function has a maximum or a minimum value. State the maximum

or minimum value. What are the domain and range of the function?

4. y = 5𝑥2 – 2x + 2 5. y = 3

2𝑥2 + 4x – 9

6. BASEBALL The equation h = –0.005𝑥2 + x + 3 describes the path of a baseball hit into the outfield, where h is the

height and x is the horizontal distance the ball travels.

a. What is the equation of the axis of symmetry?

b. What is the maximum height reached by the baseball?

c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the

outfielder catches it?

4/20 & 4/21

twhitaker

Sticky Note

Complete 4/20 and 4/21

9.2 Transformations of Quadratic Functions Notes COMPLETED

1

9.2

Transformations of Quadratic Functions

Use this lesson to complete 9.2 Skills Practice

April 22, 2020


2

Vertex Form


3

Examples


4

Examples

NAME _____________________________________________ DATE ____________________________ PERIOD _____________


9-2 Skills Practice Transformations of Quadratic Functions

Describe how the graph of each function is related to the graph of f(x) = 𝒙𝟐.

1. g(x) = 𝑥2 + 2 2. g(x) = (𝑥 − 1)2 3. g(x) = 𝑥2 – 8

4. g(x) = 7𝑥2 5. g(x) = 1

5𝑥2 6. g(x) = –6𝑥2

7. g(x) = –𝑥2 + 3 8. g(x) = 5 – 1

5𝑥2 9. g(x) = 4(𝑥 − 1)2

Match each equation to its graph.

10. y = 2𝑥2 – 2 A. C.

11. y = 1

2𝑥2 – 2

12. y = – 1

2𝑥2 + 2

13. y = –2𝑥2 + 2 B. D.

4/22 & 4/23

9.3 Solving Quadratics by Graphing Notes COMPLETED

1

9.3

Solving Quadratic Equations by Graphing

Use this lesson to complete 9.3 Practice

4/27/2020


2


3

Examples

Make sure equation is set equal to 0

Type equation in to Desmos

Your solution(s) are the x-intercepts (where the graph crosses the x-axis). These are also called

"roots" and "zeros"

(You will need to graph by hand if you don't have access to desmos or a graphing calculator)


4

Sometimes the two roots are the same number, called a double root


5

No Real Solution because it doesn't cross the x-axis


6

Application

-.015 doesn't make sense for this problem, so the solution is 4.078 seconds, rounded up to 5 because it says "approximately"

NAME _____________________________________________ DATE ____________________________ PERIOD _____________


9-3 Practice Solving Quadratic Equations by Graphing

Solve each equation by graphing. (I have already graphed them for you, you need to write the solutions)

1. 𝑥2 – 5x + 6 = 0 2. 𝑤2 + 6w + 9 = 0 3. 𝑏2 – 3b + 4 = 0

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

4. 𝑝2 + 4p = 3 5. 2𝑚2 + 5 = 10m 6. 2𝑣2 + 8v = –7

7. NUMBER THEORY Two numbers have a sum of 2 and a product of –8.

The quadratic equation –𝑛2 + 2n + 8 = 0 can be used to determine the

two numbers.

a. Graph the related function f(n) = –𝑛2 + 2n + 8 and determine its

x-intercepts.

b. What are the two numbers?

NAME _____________________________________________ DATE ____________________________ PERIOD _____________


8. DESIGN A footbridge is suspended from a parabolic support. The

function h(x) = – 1

25𝑥2 + 9 represents the height in feet of the

support above the walkway, where x = 0 represents the midpoint

of the bridge.

a. Graph the function and determine its x-intercepts.

b. What is the length of the walkway between the points where the

support intersects the walkway?

9.4 Solving Equations by Factoring Notes COMPLETED

1

9.4

Solving Quadratics by Factoring

Use this lesson to complete the EVENS on the front and back of 9.4 Study Guide

Intervention

4/29/2020


2

Square Root PropertyTo solve an equation in the form 1. isolate the squared term2. take the square root of both sides3. finish solving for the variable, if necessary

Examples: Solve the following


3

Solving Equations by Factoring*Recall that 0 times anything is 0

This is called the zero product property

Examples


4

Examples cont.

Factoring using difference of squares

Solving using square root property

NAME _____________________________________________ DATE ____________________________ PERIOD _____________


9-4 Study Guide and Intervention

Solving Quadratic Equations by Factoring

Solve Quadratic Equations Using the Square Root Property You may be able to use the Square Root Property

below to solve certain equations. The repeated factor gives just one solution to the equation.

Square Root Property For any number n > 0, if 𝑥2 = n, then x = ±√𝑛.

Example: Solve each equation. Check your solutions.

a. 𝒙𝟐 = 20

𝑥2 = 20 Original equation

x = ±√20 Square Root Property

x = ±2√5 Simplify.

The solution set is {–2√5, 2√5}. Since (– 2√5)2 = 20 and (2√5)2 = 20, the solutions check.

b. (𝒂 − 𝟓)𝟐 = 64

(𝑎 − 5)2 = 64 Original equation

a – 5 = ± √64 Square Root Property

a – 5 = ±8 64 = 8 ⋅ 8

a = 5 ± 8 Add 5 to each side.

a = 5 + 8 or a = 5 – 8 Separate into 2 equations.

a = 13 a = –3 Solve each equation.

The solution set is {–3, 13}. Since (−3 − 5)2 = 64 and (13 − 5)2 = 64, the solutions check.

Exercises

Solve each equation. Check the solutions.

1. 𝑥2 = 4 2. 16𝑛2 = 48 3. 𝑑2 = 25

4. 𝑥2 = 169 5. 9𝑥2 = 9 6. 𝑥2 = 1

4

7. 5𝑘2 = 25 8. 𝑝2 = 49 9. 𝑥2 = 64

10. 6𝑥2 = 54 11. 𝑎2 = 17 12. 𝑦2 = 8

13. (2𝑥 + 1)2 = 1 14. (4𝑥 + 3)2 = 25 15. (3ℎ − 2)2 = 4

16. (𝑥 + 1)2 = 7 17. (𝑦 − 3)2 = 6 18. (𝑚 − 2)2 = 5

NAME _____________________________________________ DATE ____________________________ PERIOD _____________


9-4 Study Guide and Intervention (continued) Solving Quadratic Equations by Factoring

Solve Equations by Factoring Factoring and the Zero Product Property can be used to solve equations that can be

written as the product of any number of factors set equal to 0.

Example: Solve each equation. Check your solutions.

a. 𝒙𝟐 + 6x = 7

𝑥2 + 6x = 7 Original equation

𝑥2 + 6x – 7 = 0 Rewrite equation so that one side equals 0.

(x – 1)(x + 7) = 0 Factor.

x – 1 = 0 or x + 7 = 0 Zero Product Property

x = 1 x = –7 Solve each equation.

Since 12 + 6(1) = 7 and (– 7)2 + 6(–7) = 7, the solution set is {1, –7}.

b. 12𝒙𝟐 + 3x = 2 – 2x

12𝑥2 + 3x = 2 – 2x Original equation

12𝑥2 + 5x – 2 = 0 Rewrite equation so that one side equals 0.

(3x + 2)(4x – 1) = 0 Factor the left side.

3x + 2 = 0 or 4x – 1 = 0 Zero Product Property

x = – 2

3 x =

1

4 Solve each equation.

The solution set is {− 2

3 ,

1

4} .

Since 12(− 2

3)

2 + 3(−

2

3) = 2 – 2(−

2

3) and 12(

1

4)

2+ 3(

1

4) = 2 – 2(

1

4), the solutions check.

Exercises Solve each equation by factoring. Check the solutions.

1. 𝑥2 – 4x + 3 = 0 2. 𝑦2 – 5y + 4 = 0 3. 𝑚2 + 10m + 9 = 0

4. 𝑥2 = x + 2 5. 𝑥2 – 4x = 5 6. 𝑥2 – 12x + 36 = 0

7. 2𝑘2 – 40 = –11k 8. 2𝑝2 = –21p – 40 9. –7 – 18x + 9𝑥2 = 0

10. 16𝑦3 = 25y 11. 1

64𝑥2 = 49 12. 4𝑎3 – 64a = 0

13. 3𝑏3 – 27b = 0 14. 9

25𝑚2 = 121 15. 48𝑛3 = 147n

Algebra 1 Packets 4/14-5/1 -- Mrs. Tackett

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Transcript of Algebra 1 Packets 4/14-5/1 -- Mrs. Tackett