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Transforming Parabolas Worksheet

Grade 9 Math worksheet focusing on transformations of parabolas, including translations, reflections, and dilations.

Grade 9 Math AlgebraTransforming Parabolas
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Includes

2 Short AnswerMultiple ChoiceFill in the BlanksTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSF.BF.B.3CCSS.MATH.CONTENT.HSF.IF.C.7.A

Topics

AlgebraParabolasTransformationsQuadratic FunctionsGrade 9
8 sections · Free to use · Printable
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Transforming Parabolas

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Date:

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Read each question carefully and follow the instructions to transform the parabolas.

1. Describe the transformation that occurs when the function f(x) = x² is changed to f(x) = (x - 3)².

2. How does the graph of y = -x² differ from the graph of y = x²?

3. Which equation represents a parabola that has been shifted 2 units up from the parent function y = x²?

a

y = (x - 2)²

b

y = x² + 2

c

y = x² - 2

d

y = (x + 2)²

4. What is the vertex of the parabola y = (x + 4)² - 1?

a

(4, 1)

b

(-4, 1)

c

(4, -1)

d

(-4, -1)

5. A parabola opens downward if the coefficient of the x² term is  .

6. The graph of y = 3x² is   than the graph of y = x².

7. The vertex of the parabola y = (x - 5)² is (5, 0).

T

True

F

False

8. A vertical stretch makes the parabola appear wider.

T

True

F

False

9. Graph the parent function y = x² and the transformed function y = -(x + 1)² + 3 on the coordinate plane below. Label both graphs.

-10-8-6-4-2246810-10-8-6-4-2246810

10. Write the equation of a parabola that opens downward, has its vertex at (2, -5), and is vertically stretched by a factor of 2.

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