Lesson 13.1 Assignment
Name
Date
Controlling the Population
Adding and Subtracting Polynomials
Ramona and James build a model rocket and two rocket launchers. Ramona’s rocket launcher can launch
the rocket with an initial velocity of 200 feet per second. James’s rocket launcher can launch the rocket
with an initial velocity of 192 feet per second. They launch the rocket using Ramona’s launcher and on its
way back down it lands on the roof of a building that is 320 feet tall. The height of the rocket can be
represented by the equation H1(x) 5 216x2 1 200x, where x represents the time in seconds and H1(x)
represents the height.
Ramona and James take the stairs to the roof of the building and re-launch the rocket using James’s
rocket launcher. The rocket lands back on the ground. The height of the rocket after this launch can
be represented by the equation H2(x) 5 216x2 1 192x 1 320.
In both functions, 216 represents the gravitational pull on the rocket in feet per second squared.
1. Compare and contrast the polynomial functions.
2. Analyze both functions.
a. Graph the functions.
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8 10 12 14 16 18
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Lesson 13.1 Assignment
page 2
b. Does it make sense in terms of the problem situation to graph the functions outside of Quadrant I?
Explain your reasoning.
c. Explain why the graphs of these functions do not intersect.
3. Ramona believes that she can add the 2 functions to determine the total height of the rocket at any
given time.
a. Write a function S(x) that represents the sum of H1(x) and H2(x). Show your work.
b. Is Ramona correct? Explain your reasoning.
4. Subtract H1(x) from H2(x) and write a new function, D(x), that represents the difference. Then, explain
what this function means in terms of the problem situation.
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218 Chapter 13 Assignments
Lesson 13.2 Assignment
Name
Date
They’re Multiplying—Like Polynomials!
Multiplying Polynomials
1. Consider the binomials (x 1 3), (2x 1 1), and (x 2 4).
a. Without multiplying, make a conjecture about the degree of the product of these binomials.
Explain how you determined your answer.
b. Without multiplying, make a conjecture about the number of terms in the product of these binomials.
Explain your reasoning.
c. Two students determine the product of the 3 binomials using two different methods. Student 1 uses
a multiplication table, and Student 2 uses the Distributive Property. Their work is shown below.
Determine which student multiplied correctly and identify the mistake the other student made.
Explain how you determined your answer.
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Student 1
Student 2
∙
x
3
2x
x
x
3x
2x
x
24
24x
212
28x
24
1
(x 1 3)(2x 1 1)(x 2 4) 5 (2x2 1 7x 1 3)(x 2 4)
5 2x3 2 x2 2 25x 2 12
2
2
The product is 3x2 2 8x 2 16.
The product is 2x3 2 x2 2 25x 2 12.
2. Consider the trinomials 2x2 2 5x 1 7 and 23x2 1 4x 2 2.
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a. Without multiplying, make a conjecture about the degree of the product of these trinomials.
Explain how you determined your answer.
b. Without multiplying, make a conjecture about the number of terms in the product of these trinomials.
Explain your reasoning.
Chapter 13 Assignments 219
Lesson 13.2 Assignment
page 2
c. Determine the product of these trinomials. Show your work.
3. Consider the binomials (5x 2 9), (4x 1 7), and (3x 2 6).
a. You now know three methods for multiplying polynomials. Which method would you prefer to use
to determine the product of these polynomials? Explain your reason.
b. Determine the product of the polynomials. Show your work.
4. Describe when each of the following methods is most helpful in multiplying polynomials.
Algebra Tiles—
Multiplication Tables—
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Distributive Property—
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220 Chapter 13 Assignments
Lesson 13.3 Assignment
Name
Date
What Factored Into It?
Factoring Polynomials
1. Mr. Vanek writes the trinomial 6x2 1 26x 1 28 on the board and asks Wanda and Cyril to factor it.
Their work is shown below. Determine which student factored the trinomial correctly. Identify any
mistakes that were made in either solution and correct them.
Wanda
Cyril
6x 1 26x 1 28 5 (3x 1 7)(2x 1 4)
6x2 1 26x 1 28 5 2(3x2 1 13x 1 14)
5 2(3x 1 7)(x 1 2)
2
2. Without factoring, determine the signs of the binomial factors of each trinomial in the table below.
Explain how you determined each answer.
Trinomial
Signs of Binomial Factors
Explanation
x2 1 3x 2 18
x2 2 9x 1 18
x2 2 3x 2 18
x2 1 9x 1 18
3. Consider the trinomial 22x2 1 5x 1 12.
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a. Kevin claims that the binomial factors will both be positive. Is Kevin correct? Why or why not?
b. Angelica claims that she can rewrite the trinomial as 12 1 5x 2 2x2 to determine the signs of the
binomial factors. Is she correct? If so, determine the signs of the binomial factors. If not, explain
why not.
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c. Verify your answer to part (b) by factoring the trinomial completely. Show your work.
Chapter 13 Assignments 221
Lesson 13.3 Assignment
page 2
4. Complete the following multiplication table. Then, write the trinomial and its factors. Explain how you
determined your answers.
∙
x
x
23x
224
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5. The area of a rectangle is represented by the quadratic expression 6x2 2 x 215. Determine the
expressions that can be used to represent the length and width of the rectangle. Then, explain how
you determined your answer.
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222 Chapter 13 Assignments
Lesson 13.4 Assignment
Name
Date
Zeroing In
Solving Quadratics by Factoring
Solve each quadratic equation. Show your work.
1. x(x 1 3) 2 100 5 3x
2. 4(x 1 1)2 5 8(x 1 1)
3. The area of a rectangle is given by the quadratic equation A 5 x2 1 2x 2 63.
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a. Solve the quadratic equation. Explain what the solution(s) mean(s) in terms of the problem situation.
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Chapter 13 Assignments 223
Lesson 13.4 Assignment
page 2
b. Graph the equation. Identify the vertex, x- and y-intercepts, and the line of symmetry. Label them
on the graph and then explain what each one means in terms of the problem situation.
10
0 2
28 26 24 22
210
4
6
8
x
220
230
240
250
260
Vertex:
x-intercepts:
y-intercept:
Line of symmetry:
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c. Kata claims that x can be equal to 9. Is she correct? If so, explain why and then determine the
length, width, and area of the rectangle. If not, explain why not.
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224 Chapter 13 Assignments
Lesson 13.5 Assignment
Name
Date
What Makes You So Special?
Special Products
1. Ms. Frances writes the expression 36x2 2 100 on the board and asks her students to factor it
completely. The work of two of her students, Justin and Nakia, is shown. Determine which student
factored the expression correctly. Then, identify the mistake the other student made.
Explain how you determined your answers.
Justin
36x 2 100 5 (6x 1 10)(6x 2 10)
5 2(3x 1 5)(3x 2 5)
2
Nakia
36x2 2 100 5 4(9x2 2 25)
5 4(3x 1 5)(3x 2 5)
4  ​x2 1 __
2. Is the expression ​ __
​ 4 ​ x 1 1 a perfect square trinomial? Explain how you determined your answer.
9
3
If possible, factor the expression completely.
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3. N
ina claims that the expression 3x2 2 24 is the difference of two cubes. Perry argues that it is not.
Who is correct? Explain your reasoning. If possible, factor the expression completely.
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Chapter 13 Assignments 225
Lesson 13.5 Assignment
page 2
4. Ms. Morrison writes the expression r12 2 64 on the board. Kitsy says that the expression is the
difference of two squares. Angel argues that it is the difference of two cubes. Their work is shown
below. Who factored the expression correctly? Explain how you determined your answer. Support
your answer by checking Kitsy’s and Angel’s work.
Kitsy’s Work
r12 2 64 5 (r 6 2 8)(r 6 1 8)
5 (r 2 2 2)(r 4 1 2r 2 1 4) (r 2 1 2)(r 4 2 2r 2 1 4)
Angel’s Work
r12 2 64 5 (r 4 2 4)(r 8 1 4r 4 1 16)
5 (r 2 1 2)(r 2 2 2)(r 8 1 4r 4 1 16)
5. Mr. Peters writes the expression b15 1 125 on the board. Galen says that the expression is the sum of
two cubes. Paul argues that it can’t be the sum of two cubes, because 15 is not a perfect cube. Who
is correct? Explain your reasoning. If possible, factor the expression completely.
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226 Chapter 13 Assignments
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5 (r 2 2 2)(r 2 1 2)(r 4 1 2r 2 1 4)(r 4 2 2r 2 1 4)
Lesson 13.6 Assignment
Name
Date
Could It Be Groovy to Be a Square?
Approximating and Rewriting Radicals
1. Zi wants to use paving stones to create a circular patio in her backyard. She knows that she has
enough stones to cover 345.4 square feet. Estimate the maximum diameter Zi can make her patio.
Use 3.14 for p. Show your work.
2. You can approximate the square roots of numbers that are not perfect squares.
a. Determine the approximate value of the square root of 14. Show your work.
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b. Gabriel claims that you can use the algorithm below to approximate the square root of a number.
The work for how to use Gabriel’s algorithm to determine the square root of 14 is shown.
Step 1
Starting number
14
Step 2
Guess what the square root might be.
3.5
Step 3
Divide the starting number by your guess.
Step 4
Calculate the average of your guess and the
quotient of Step 3.
3.5 1
4 
​ _______
 
 ​
5 3.75
2
Use the result of Step 4 as your new guess
and repeat Steps 3 and 4.
14 4 3.75 < 3.73333
Step 5
14 4 3.5 5 4
13
3.75 1 3.73333
    
​ _______________
 ​
< 3.74167
2
How do your results compare to Gabriel’s results?
Chapter 13 Assignments 227
Lesson 13.6 Assignment
page 2
c. Analyze Gabriel’s algorithm, and explain why it works.
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d. Use Gabriel’s algorithm to calculate the square root of 29. Show your work.
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228 Chapter 13 Assignments
Lesson 13.6 Assignment
page 3
Name
Date
3. Michael is installing new baseboard in his living room. The living room is a square and he knows that
it is 720 square feet. He needs to determine the length of each wall, so that he’ll know how long each
piece of baseboard needs to be.
a. Determine the exact length of the baseboard for each wall. Show your work.
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b. Will determining the exact length or an approximate length be most helpful in cutting the
baseboard? Explain your reasoning.
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Chapter 13 Assignments 229
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230 Chapter 13 Assignments
Lesson 13.7 Assignment
Name
Date
Another Method
Completing the Square
1. Determine the roots of the equation y 5 x2 1 9x 1 3. Check your solutions.
2. Consider the equation y 5 2x2 1 10x 2 8.
a. Graph the equation.
y
8
4
212
28
0
24
4
x
24
28
212
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216
220
224
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228
Chapter 13 Assignments 231
Lesson 13.7 Assignment
page 2
b. Use the graph to estimate the solutions to the equation. Explain how you determined your answer.
c. Two students completed the square to determine the solutions to this equation. Their work is
shown below. Which student is correct? Explain your reasoning.
Student 1
Student 2
y 5 2x2 1 10x 2 8
y 5 2x2 1 10x 2 8
2x2 1 10x 2 8 5 0
2x2 1 10x 2 8 5 0
2
2 8​ 
_____________
​ 2x 1 10x
    
50
2
x2 1 5x 5 4
x2 1 5x 1 ___
​ 25 ​ 5 4 1 ___
​ 25 ​ 
4
4
2
5
41
​   ​  ​ 5 ___
​   ​ 
​ x 1 __
2
4
2x2 1 10x 5 8
2x2 1 10x 1 25 5 8 1 25
(2x 1 5)2 5 33
2x 1 5 5 6​√ 33 ​ 
________
___
5 6​√ 33 ​ 
√​ (2x 1 5)2 ​ 
___
___
√
​ 33 ​  
x 5 __________
​ 25 6  ​
 
2
x < 25.372 or x < 0.372
(  )
___

​ 5 ​ )​ ​ 
5 6​√___
​ 41 ​ ​  
​  ​( x 1 __
4
 2
___
 
 
2
√
​ 41  ​
x 1 __
​ 5 ​5 6​ ____
 
  
​
2 ___
2
√
 
x 5 __________
​ 25 6  ​ 41  ​ 
​
2
x < 25.702 or x < 0.702
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232 e. Write a statement about the value of the coefficient of the x2-term before you can complete the
square.
Chapter 13 Assignments
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d. Compare the different solutions. Identify what the student who got the correct answer did that
allowed him or her to correctly complete the square.
Lesson 13.7 Assignment
page 3
Name
Date
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3. Determine the roots of the equation y 5 3x2 1 24x 2 6. Check your solutions.
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Chapter 13 Assignments 233
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234 Chapter 13 Assignments