AnswersApplications and ModelingQuadratic Equations

Quadratic Equations Answers

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Graph the function. y = -6x2 - 12x -1 a. c. b. Please select the best answer from the choices provided

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A
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C
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Given a quadratic function, , what happens to the graph when "a" is positive?

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the parabola opens down, the vertex is the maximum value
B
the parabola opens down, the vertex is the minimum value
C
the parabola opens up, the vertex is the maximum value
D
the parabola opens up, the vertex is the minimum value
3

Graph the function. y = 2x2 + 4x a. c. b. Please select the best answer from the choices provided

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A
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B
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C
4

Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.

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both f and g open downward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
B
both f and g open upward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
C
both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
D
both f and g open downward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
5

In the following function defined by an equation in the form , identify the values of a, b, and c. a. b. c. d. Please select the best answer from the choices provided

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A
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B
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C
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D
6

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 -2 0 4 down (0,-2) Table B a b c up or down y-intercept 4 0 -2 down (0,4) Table C a b c up or down y-intercept -4 0 -2 down (0,-2) Table D a b c up or down y-intercept -2 0 4 down (0,4)

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Table A
B
Table B
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Table C
D
Table 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 0 0 7 up (0, 7) Table B a b c up or down y-intercept 7 0 0 up (0, 0) Table C a b c up or down y-intercept 7 0 0 up (0, 7) Table D a b c up or down y-intercept 0 7 0 up (0, 0)

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Table A
B
Table B
C
Table C
D
Table D
8

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:

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A
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B
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C
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D
9

All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at what point?

A
vertex
B
function
C
translation
D
y-intercept
10

In the following function defined by an equation in the form , identify the values of a, b, and c. a. b. c. d. Please select the best answer from the choices provided

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A
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B
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C
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D
11

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.)

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A
-shaped; y-intercept (5, 0); symmetrical with respect to the y-axis
B
-shaped; y-intercept (0, -5); symmetrical with respect to the y-axis
C
-shaped; y-intercept (0, -5); symmetrical with respect to the y-axis
D
-shaped; y-intercept (5, 0); symmetrical with respect to the y-axis
12

Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.

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both open upward; h is wider than f
B
both open downward; h is narrower than f
C
h opens downward; f opens upward; h is wider than f
D
h opens upward; f opens downward; h is narrower than f
13

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, 6); symmetrical with respect to the y-axis
B
-shaped; y-intercept (0, 6); symmetrical with respect to the y-axis
C
-shaped; y-intercept (6, 0); assymmetrical with respect to the y-axis
D
-shaped; y-intercept (0, 6); assymmetrical with respect to the y-axis
14

Graph the function. y = a. c. b. Please select the best answer from the choices provided

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A
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B
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C
15

In the following function defined by an equation in the form , identify the values of a, b, and c. a. b. c. d. Please select the best answer from the choices provided

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A
B
B
C
C
D
D
16

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 3 2 -8 up (0,-8) Table B a b c up or down y-intercept 3 2 8 up (0,-8) Table C a b c up or down y-intercept 3 2 8 up (0,8) Table D a b c up or down y-intercept 3 2 -8 down (0,-8)

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Table A
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Table B
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Table C
D
Table D
17

Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.

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A
h is g shifted down 3 units; both open upward
B
h is g shifted up 3 units; both open upward
C
h is g shifted up 3 units; both open downward
D
h is g shifted down 3 units; both open downward
18

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 8 0 -8 down (0,-8) Table B a b c up or down y-intercept 8 0 -8 up (0,8) Table C a b c up or down y-intercept -8 0 8 up (0,-8) Table D a b c up or down y-intercept 8 0 –8 up (0,-8)

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Table A
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Table B
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Table C
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Table D

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