Graphing Parabolas

A Grade 10 math worksheet focusing on graphing parabolas, identifying key features, and understanding transformations.

Grade 10 Math AlgebraGraphing Parabolas

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / FalseLong Answer

Standards

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

Topics

AlgebraParabolasQuadratic FunctionsGraphing

8 sections · Free to use · Printable

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Graphing Parabolas

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Read each question carefully and follow the instructions to graph parabolas and identify their key features. Show all your work for full credit.

1. Graph the function y = x² on the coordinate plane below. Identify the vertex and axis of symmetry.

Vertex:

Axis of Symmetry:

For the parabola y = 2(x - 3)² + 1:

2. The vertex of the parabola is at .

3. The axis of symmetry is the line .

4. The parabola opens (upwards/downwards).

5. Which of the following functions represents a parabola that is wider than y = x² and opens downwards?

y = -2x²

y = -0.5x²

y = x² + 3

y = (x + 1)²

6. The graph of y = (x - 4)² has its vertex at (4, 0).

True

False

7. Adding a positive constant 'c' to y = ax² + c shifts the parabola 'c' units to the left.

True

False

8. Graph the function y = -(x + 2)² - 3 on the coordinate plane below. Label the vertex and axis of symmetry.

Vertex:

Axis of Symmetry:

9. Describe the transformations applied to the parent function y = x² to obtain the function y = 3(x - 1)² + 5. Be specific about the direction and magnitude of each transformation.