Graphing Parabolas

This worksheet focuses on graphing parabolas, identifying key features such as vertex, axis of symmetry, focus, and directrix, and writing equations from given information.

Grade 11 Math AlgebraGraphing Parabolas

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Includes

Short AnswerGraphFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.ACCSS.MATH.CONTENT.HSG.GPE.A.2

Topics

parabolagraphingalgebrapre-calculusconic sections

7 sections · Free to use · Printable

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Graphing Parabolas Worksheet

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Carefully read each question and follow the instructions. Show all your work for full credit.

1. For the parabola y = (x - 3)² + 2, identify the following:

a. Vertex:

b. Axis of Symmetry:

c. Direction of Opening:

2. For the parabola x = -2(y + 1)² - 4, identify the following:

a. Vertex:

b. Axis of Symmetry:

c. Direction of Opening:

3. Graph the parabola y = x² - 4x + 3 on the coordinate plane below. Label the vertex and axis of symmetry.

4. Graph the parabola x = -(y - 2)² + 1 on the coordinate plane below. Label the vertex and axis of symmetry.

5. Write the equation of a parabola with vertex (1, -5) and focus (1, -3).

Equation:

6. Write the equation of a parabola with focus (-2, 4) and directrix x = -6.

Equation:

7. Which of the following parabolas opens downwards?

y = 2x² - 3x + 1

y = -x² + 5x - 2

x = (y - 4)² + 3

x = -3(y + 1)² + 6

8. The vertex of the parabola y = -3(x + 2)² - 5 is (-2, -5).

True

False

9. A parabola with a directrix of y = 3 opens upwards.

True

False