AnswersPBCSD_Grade_Forgiveness_1200710_Mathematics_for_College_Algebra_S2_2023Unit Test

Modeling with Quadratic Functions Answers

10 verified answers2 views
1
Free Preview

On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.Time (x) Height (y) 0102241610How high was the ball after 8 seconds?

A
20 feet
B
42 feet
C
96 feet
D
106 feet
2
Free Preview

The function f(x) = –(x – 20)(x – 100) represents a company’s monthly profit as a function of x, the number of purchase orders received. Which number of purchase orders will generate the greatest profit?

A
20
B
60
C
80
D
100
3

The graph shows the function representing the recommended amount of mulch, in cubic yards, for circular flowerbeds based on the radius of the flowerbed in feet.

Question illustration
A
7 cubic yards
B
13 cubic yards
C
26 cubic yards
D
31 cubic yards
4

The zeros of a parabola are -5 and -3. The point (0, 60) is on the graph as represented by the equation. 60=a(0+5)(0+3)

A
−7.5
B
−4
C
4
D
7.5
5

A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (–4, 0) and (6, 0). The y-intercept of the first parabola is (0, –12). The y-intercept of the second parabola is (0, –24). What is the positive difference between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to the nearest tenth.

Answer not available
6

The vertex of a quadratic function is (6, 2), and the y-intercept of the function is (0, −70). The equation of the function in vertex form, f(x)=a(x−h)2+k, is shown.−70=a(0−6)2+2

A
−6
B
−2
C
2
D
6
7

The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?

A
y = (x – 2)(x + 3)
Option A
B
y = (x – 2)(x + 3)
Option B
C
y = (x + 2)(x – 3)
Option C
D
y = (x + 2)(x – 3)
Option D
8

Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)?

A
f(x) = −6(x + 1)(x + 5)
B
f(x) = −6(x − 1)(x − 5)
C
f(x) = −5(x + 1)(x + 5)
D
f(x) = −5(x − 1)(x − 5)
9

Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.

Question illustration
A
y = –17(x)(x – 4)
B
y = –16(x)(x – 4)
C
y = –16(x – 2)2 + 68
D
y = –17(x – 2)2 + 68
10

Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a function of time, x, in seconds. What is the maximum height the ball reaches?

A
2 feet
B
16 feet
C
32 feet
D
64 feet
11

Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.

Question illustration
A
y = –17(x)(x – 4)
B
y = –16(x)(x – 4)
C
y = –16(x – 2)2 + 68
D
y = –17(x – 2)2 + 68
12

A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?

A
14 inches
B
15 inches
C
28 inches
D
30 inches
13

The table shows the approximate height of a projectile x seconds after being fired into the air.

Question illustration
A
y = –10(x)(x – 5)
B
y = 10(x)(x – 5)
C
y = –10(x – 5)
D
y = 10(x – 5)
14

The zeros of a parabola are –4 and 2, and (6, 10) is a point on the graph. Which equation can be solved to determine the value of a in the equation of the parabola?

A
6 = a(10 – 4)(10 + 2)
B
6 = a(10 + 4)(10 – 2)
C
10 = a(6 – 4)(6 + 2)
D
10 = a(6 + 4)(6 – 2)
15

The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground?

A
30 meters
B
40 meters
C
50 meters
D
60 meters
16

Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a function of time, x, in seconds. What is the maximum height the ball reaches?

A
2 feet
B
16 feet
C
32 feet
D
64 feet
17

The minimum of a parabola is located at (–1, –3). The point (0, 1) is also on the graph. Which equation can be solved to determine the a value in the function representing the parabola?

A
1 = a(0 + 1)2 – 3
B
1 = a(0 – 1)2 + 3
C
0 = a(1 + 1)2 – 3
D
0 = a(1 – 1)2 + 3
18

The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far away from the maximum depth is a point on the mirror that is inches in depth?

Question illustration
A
3 inches
B
4 inches
C
5 inches
D
6 inches
19

The graph shows the function representing the recommended amount of mulch, in cubic yards, for circular flowerbeds based on the radius of the flowerbed in feet.

Question illustration
A
7 cubic yards
B
13 cubic yards
C
26 cubic yards
D
31 cubic yards
20

The zeros of a parabola are -5 and -3. The point (0, 60) is on the graph as represented by the equation. 60=a(0+5)(0+3)

A
−7.5
B
−4
C
4
D
7.5

Did you find these answers helpful?

More from this Course

Quiz
21 verified answers

Introduction to Quadratic Functions

Quiz
25 verified answers

Quadratic Functions: Standard Form

Quiz
19 verified answers

Quadratic Functions: Factored Form