Calculating The Volume Worksheet Page 4
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414. Determine the vertex of each quadratic function given in vertex form. NO CALC. You must show your work
2
1
a.�� ( �� ) = −4 ( �� + 9 )
− 2
2
b.�� ( �� ) =
(�� − 5)
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15. Use your calculator to determine the vertex of each quadratic function given in standard form. Rewrite the
function in vertex form.
2
2
a.�� ( �� ) = ��
− 10�� + 24
b. �� ( �� ) = −2��
− 14�� − 12
16. Use your calculator to determine the x-intercepts of each quadratic function given in standard form. Rewrite the
function in factored form.
2
1
a.�� ( �� ) = 2��
+ 18�� + 16
2
b.�� ( �� ) =
��
− 2��
3
17. Write an equation for a quadratic function with each set of given characteristics. NO Calculator
a. The vertex is (0,8) and the parabola opens down
b. The x-intercepts are 5 and 12 and the parabola opens
with a vertical stretch (dilation) of 2.
up with a vertical stretch (dilation) of one-half.
d. The vertex is (3, -2) and the parabola opens up with
c. The x-intercepts are -3 and 4 and the parabola opens
down.
a vertical stretch (dilation) of 4.
18. For each of the following, describe the vertex, concavity and stretch, then sketch the functions on the graph
provided. You must show the vertex and four other exact points for each function. NO Calculator
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2
a. �� ( �� ) = (�� − 2)
b.�� ( �� ) = −��
− 3
+ 4
y
y
Vertex:
Vertex:
Concavity:
Concavity:
x
x
Stretch:
Stretch:
2
2
c. �� ( �� ) = 3��
d. �� ( �� ) = −2 ( �� − 1 )
− 5
+ 4
y
y
Vertex:
Vertex:
Concavity:
Concavity:
x
x
Stretch:
Stretch:
19. Use trig identities for the following problems.
2
2
��������
sin
��+cos
��
b. Prove: (
) ( �������� ) = 1
a. Simplify:
��������
��������
20. Show triangles with your solutions. Or use the unit circle!
b. �������� = 0, where 0 ≤ �� < 2��
2 √ 3
a. �������� = −
, where 0 ≤ �� < 2��
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