algebra 1 packets 4/14-5/1 -- mrs. tackett
TRANSCRIPT
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
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
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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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:
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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Identify Characteristics from a Given Graph
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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Identify Characteristics from a Given Function
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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Maximum and Minimum Values
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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Maximum and Minimum Values
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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Application
9.1 Characteristics and Graphing Quadratics Notes COMPLETED
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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
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
9.2 Transformations of Quadratic Functions Notes COMPLETED
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Vertex Form
9.2 Transformations of Quadratic Functions Notes COMPLETED
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Examples
9.2 Transformations of Quadratic Functions Notes COMPLETED
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Examples
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Chapter 9 13 Glencoe Algebra 1
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
9.3 Solving Quadratics by Graphing Notes COMPLETED
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9.3 Solving Quadratics by Graphing Notes COMPLETED
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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)
9.3 Solving Quadratics by Graphing Notes COMPLETED
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Sometimes the two roots are the same number, called a double root
9.3 Solving Quadratics by Graphing Notes COMPLETED
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No Real Solution because it doesn't cross the x-axis
9.3 Solving Quadratics by Graphing Notes COMPLETED
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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 _____________
Chapter 9 20 Glencoe Algebra 1
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 _____________
Chapter 8 32 Glencoe Algebra 1
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
9.4 Solving Equations by Factoring Notes COMPLETED
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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
9.4 Solving Equations by Factoring Notes COMPLETED
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Solving Equations by Factoring*Recall that 0 times anything is 0
This is called the zero product property
Examples
9.4 Solving Equations by Factoring Notes COMPLETED
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Examples cont.
Factoring using difference of squares
Solving using square root property
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Chapter 9 23 Glencoe Algebra 1
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 _____________
Chapter 9 24 Glencoe Algebra 1
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