# Algebra 2

## Educators

RM
HD
JT

Problem 1

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$y=x+4$$

RM
Rithvik M.

Problem 2

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$y=2 x^{2}-(3 x-5)$$

HD
Harrison D.

Problem 3

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$y=3 x(x-2)$$

RM
Rithvik M.

Problem 4

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$f(x)=x^{2}-7$$

HD
Harrison D.

Problem 5

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$y=(x-2)(x+5)$$

RM
Rithvik M.

Problem 6

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$g(x)=-7(x-4)$$

HD
Harrison D.

Problem 7

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$h(x)=(3 x)(2 x)+6$$

RM
Rithvik M.

Problem 8

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$y=x(1-x)-\left(1-x^{2}\right)$$

HD
Harrison D.

Problem 9

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.
$$f(x)=-x(2 x+8)$$

RM
Rithvik M.

Problem 10

Identify the vertex and the axis of symmetry of each parabola.
(GRAPH NOT COPY)

HD
Harrison D.

Problem 11

Identify the vertex and the axis of symmetry of each parabola.
(GRAPH NOT COPY)

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Problem 12

Identify the vertex and the axis of symmetry of each parabola.
(GRAPH NOT COPY)

HD
Harrison D.

Problem 13

Identify the vertex and the axis of symmetry of each parabola.
(GRAPH NOT COPY)

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Problem 14

Identify the vertex and the axis of symmetry of each parabola.
(GRAPH NOT COPY)

HD
Harrison D.

Problem 15

Identify the vertex and the axis of symmetry of each parabola.
(GRAPH NOT COPY)

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Problem 16

Find a quadratic function that includes each set of values.
$$(1,-2),(2,-2),(3,-4)$$

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Problem 17

Find a quadratic function that includes each set of values.
$$(1,-2),(2,-4),(3,-4)$$

JT
Josh T.

Problem 18

Find a quadratic function that includes each set of values.
$$(-1,6),(1,4),(2,9)$$

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Problem 19

Find a quadratic function that includes each set of values.
(GRAPH NOT COPY)

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Problem 20

Find a quadratic function that includes each set of values.
(GRAPH NOT COPY)

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Problem 21

Physics A man throws a ball off the top of a building. The table shows the height of the ball at different times.
a. Find a quadratic model for the data.
b. Use the model to estimate the height of the ball at 2.5 seconds.

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Problem 22

Communications The table shows the percent of U.S. houses with cable TV.
a. Find a quadratic model using 1960 as year $0,1970$ as year $10,$ and so on.
b. Use the model to estimate the percent of households with cable $\mathrm{TV}$ in 1995

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Problem 23

Determine whether a quadratic model exists for each set of values. If so, write the model.
$$f(-2)=16, f(0)=0, f(1)=4$$

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Problem 24

Determine whether a quadratic model exists for each set of values. If so, write the model.
$$f(0)=5, f(2)=3, f(-1)=0$$

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Problem 25

Determine whether a quadratic model exists for each set of values. If so, write the model.
$$f(-1)=-4, f(1)=-2, f(2)=-1$$

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Problem 26

Determine whether a quadratic model exists for each set of values. If so, write the model.
$$f(-2)=7, f(0)=1, f(2)=0$$

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Problem 27

Identify the vertex and the axis of symmetry for each function.
(GRAPH NOT COPY)

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Problem 28

Identify the vertex and the axis of symmetry for each function.
(GRAPH NOT COPY)

HD
Harrison D.

Problem 29

Identify the vertex and the axis of symmetry for each function.
(GRAPH NOT COPY)

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Problem 30

a. Geometry Copy and complete the table. It shows the total number of segments that can be drawn among $x$ points, no three of which are collinear.
b. Write a quadratic model for the data.
c. Predict the number of segments that can be drawn among ten points.

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Problem 31

a. Postal Rates Find a quadratic model for the data. Use 1974 as year 0 .
b. Describe a reasonable domain and range for your model. (Hint: This is a discrete, real situation.)
c. Estimation Estimate when first-class postage was 29 $\mathrm{d}$ .
d. Use your model to predict when first-class postage will be 50 $\mathrm{d}$ . Explain why your prediction may not be valid.

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Problem 32

The graph of each function contains the given point. Find the value of $c .$
$$y=x^{2}+c ;(0,3)$$

HD
Harrison D.

Problem 33

The graph of each function contains the given point. Find the value of $c .$
$$y=x^{2}-c ;(4,8)$$

RM
Rithvik M.

Problem 34

The graph of each function contains the given point. Find the value of $c .$
$$y=-5 x^{2}+c ;(2,-14)$$

HD
Harrison D.

Problem 35

The graph of each function contains the given point. Find the value of $c .$
$$y=2 x^{2}+c ;\left(-\frac{3}{4},-\frac{1}{4}\right)$$

RM
Rithvik M.

Problem 36

The graph of each function contains the given point. Find the value of $c .$
$$y=-\frac{3}{4} x^{2}+c ;\left(3,-\frac{1}{2}\right)$$

HD
Harrison D.

Problem 37

The graph of each function contains the given point. Find the value of $c .$
$$y=(x+c)^{2} ;(10,0)$$

RM
Rithvik M.

Problem 38

Road Safety The table below gives the stopping distance for an automobile under certain road conditions.
a. Find a linear model for the data.
b. Find a quadratic model for the data.
c. Writing Compare the models. Which is better? Explain.

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Problem 39

Open-Ended Write three different quadratic functions, each with a graph that includes $(0,0)$ and $(5,-1) .$

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Problem 40

Critical Thinking What is the minimum number of data points you need to find a quadratic model for a data set? Explain.

HD
Harrison D.

Problem 41

How are the graphs of $y=x^{2}$ and $y=|x|$ similar? How are they different?

RM
Rithvik M.

Problem 42

A parabola contains the points $(0,-4),(2,4),$ and $(4,4) .$ Find the vertex.

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Problem 43

A model for the height of an arrow shot into the air is $h(t)=-16 t^{2}+72 t+5$ where $t$ is time and $h$ is height. Without graphing, consider the function's graph.
a. What can you learn by finding the graph's intercept with the $h$ -axis?
b. What can you learn by finding the graph's intercept(s) with the $t$ -axis?

Tony N.

Problem 44

For which quadratic function is $-3$ the constant term?
A. $y=(3 x+1)(-x-3)$
C. $f(x)=(x-3)(x-3)$
B. $y=x^{2}-3 x+3$
D. $g(x)=-3 x^{2}+3 x+9$

HD
Harrison D.

Problem 45

The vertex of a parabola is $(3,2)$ . A second point on the parabola is $(1,7)$ . Which point is also on the parabola?
F. $(-1,7)$
G. $(3,7)$
H. $(5,7)$
J. $(3,-2)$

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Problem 46

The graph of a quadratic function has vertex $(-3,-2) .$ What is the axis of symmetry?
$$\begin{array}{llll}{\text { A. } x=-3} & {\text { B. } x=3} & {\text { c. } y=-2} & {\text { D. } y=2}\end{array}$$

HD
Harrison D.

Problem 47

Which function is NOT a quadratic function?
F. $y=(x-1)(x-2)$
H. $y=3 x-x^{2}$
G. $y=x^{2}+2 x-3$
J. $y=-x^{2}+x(x-3)$

RM
Rithvik M.

Problem 48

What is the quadratic function with a graph that includes $(1,6),(2,11),$ and $(3,20) ?$ Find the function by writing and solving a system of equations. Write the function in standard form. Show all your work.

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Problem 49

Write the augmented matrix for each system. Then solve the system.
$$\left\{\begin{array}{l}{3 x-y=7} \\ {2 x+2 y=10}\end{array}\right.$$

RM
Rithvik M.

Problem 50

Write the augmented matrix for each system. Then solve the system.
\left\{\begin{aligned} 3 x+y-2 z &=-3 \\ x-3 y-z &=-2 \\ 2 x+2 y+3 z &=11 \end{aligned}\right.

HD
Harrison D.

Problem 51

Find each product.
$$\left[\begin{array}{cc}{2} & {-3}\end{array}\right]\left[\begin{array}{rrrr}{3} & {-2} & {4} & {1} \\ {2} & {0} & {-3} & {2}\end{array}\right]$$

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Problem 52

Find each product.
$$\left[\begin{array}{rr}{3} & {10} \\ {1} & {5}\end{array}\right]\left[\begin{array}{rr}{-7} & {2} \\ {8} & {4}\end{array}\right]$$

HD
Harrison D.

Problem 53

Solve each system by elimination.
$$\left\{\begin{array}{c}{x+y=7} \\ {5 x-y=5}\end{array}\right.$$

RM
Rithvik M.

Problem 54

Solve each system by elimination.
$$\left\{\begin{array}{l}{2 x-3 y=-14} \\ {3 x-y=7}\end{array}\right.$$

HD
Harrison D.

Problem 55

Solve each system by elimination.
$$\left\{\begin{array}{l}{x-3 y=2} \\ {x-2 y=1}\end{array}\right.$$

RM
Rithvik M.

Problem 56

For each direct variation, find the value of $y$ when $x=2$
$$y=2 \text { when } x=5$$

HD
Harrison D.

Problem 57

For each direct variation, find the value of $y$ when $x=2$
$$y=1 \text { when } x=4$$

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Problem 58

For each direct variation, find the value of $y$ when $x=2$
$$y=-2 \text { when } x=4$$

HD
Harrison D.