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

Transforming Parabolas

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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?

y = (x - 2)²

y = x² + 2

y = x² - 2

y = (x + 2)²

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

(4, 1)

(-4, 1)

(4, -1)

(-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).

True

False

8. A vertical stretch makes the parabola appear wider.

True

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