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Linear Programming — Unit test Answers

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What are the x-intercepts of the function f(x) = –x2 – x + 2?

A
(–2, 0) and (1, 0)
B
(2, 0) and (1, 0)
C
(–2, 0) and (-1, 0)
D
(0, -2) and (0, 1)
2
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On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).

Question illustration
A
The domain is all real numbers. The range is {y|y < 16}.
B
The domain is all real numbers. The range is {y|y ≤ 16}.
C
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
D
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
3

Which function is a quadratic function?

A
y – 3x2 = 3(x2 + 5) + 1
B
y2 – 7x = 2(x2 + 6) + 7
C
y – 2x2 = 6(x3 + 5) – 4
D
y – 5x = 4(x + 5) + 9
4

What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

On a coordinate plane, a parabola opens up. It starts in quadrant 1, crosses the x axis where the vertex is in quadrant 4, and crosses the x-axis back into quadrant 1.

Question illustration
A
f(x) = (x – 8)2 + 6
B
f(x) = (x + 8)2 + 6
C
f(x) = (x + 8)2 – 6
D
f(x) = (x – 8)2 – 6
6

Solve the following equation algebraically: a. b. c. d. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
7

For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: Table A a b c up or down y-intercept 1 -6 0 up (0,0) Table B a b c up or down y-intercept 1 0 0 up (0,-6) Table C a b c up or down y-intercept 1 6 0 up (0,0) Table D a b c up or down y-intercept 1 -6 0 down (0,0)

Question illustration
A
Table A
B
Table B
C
Table C
D
Table D
8

Solve the following equation by first writing the equation in the form : a. b. c. d. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
9

Predict what the graph of the following quadratic function will look like. (If you have a graphing calculator, you can use it to verify your prediction.)

Question illustration
A
-shaped; y-intercept (0, 1); symmetrical with respect to the y-axis
B
-shaped; y-intercept (0, 1); symmetrical with respect to the y-axis
C
-shaped; y-intercept (1, 0); assymmetrical with respect to the y-axis
D
-shaped; y-intercept (1, 0); assymmetrical with respect to the y-axis
10

Which function has an axis of symmetry of x = −2?

A
f(x) = (x − 1)2 + 2
B
f(x) = (x + 1)2 − 2
C
f(x) = (x − 2)2 − 1
D
f(x) = (x + 2)2 − 1
11

Which graph represents the function f(x) = –x2 + 5?

A
On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9).
Option B
C
On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).
Option D
12

On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6).

Question illustration
A
g(x) = (x + 5)2 + 2
B
g(x) = (x + 2)2 + 5
C
g(x) = (x – 2)2 + 5
D
g(x) = (x – 5)2 + 2
13

What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

A
(−4, 18)
B
(0, -2)
C
(-8, -2)
D
(−4, −18)
14

Which is the graph of f(x) = x2 – 2x + 3?

A
On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (2, negative 1), and goes through (4, 3).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3).
Option D
15

Which function is a quadratic function?

A
a(x) = –2x3 + 2x – 6
B
b(x) = 5x3 + 8x2 + 3
C
c(x) = –8x2 + 3x – 5
D
d(x) = 6x4 + 2x – 3
16

A soccer ball is kicked upward from a hill and then falls to the ground. The height, in feet, of the ball after t sec is modeled by the function h(t) = –16t2 + 26t +12. What is the initial height of the ball?

A
–16 ft
B
–12 ft
C
12 ft
D
22 ft
17

What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?

A
(0, –5)
B
(0, –3)
C
(0, 3)
D
(0, 5)
18

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 16), has a y-intercept at (0, negative 12), and goes through (2, 0).

Question illustration
A
(–6, 0), (2,0)
B
(–2, –16), (0, –12)
C
(–6, 0), (–2, –16), (2, 0)
D
(0, –12), (–6, 0), (2, 0)
19

The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?

A
15.21 yd
B
19.5 yd
C
38.94 yd
D
45.63 yd
20

Complete the following table using the equation: x -2 -1 0 1 2 y Plot the points on a graph and determine which graph best represents the equation. Graph A Graph B

Question illustration
A
8, 2, 0, 2, 8; Graph A
B
-8, -2, 0, -2, -8; Graph A
C
8, 2, 0, 2, 8; Graph B
D
-8, -2, 0, -2, -8; Graph B

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