Parabola Exploration Worksheet

A Grade 10 math worksheet focusing on understanding and analyzing parabolas, including their equations, vertices, foci, and directrices.

Grade 10 Math AlgebraConic SectionsParabola

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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

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

Topics

parabolaconic sectionsalgebragrade 10math

7 sections · Free to use · Printable

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Date:

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Which of the following is the standard form equation of a parabola that opens upwards or downwards?

(x - h)² = 4p(y - k)

(y - k)² = 4p(x - h)

Ax + By = C

x² + y² = r²

2. What is the focus of the parabola y² = 12x?

(3, 0)

(-3, 0)

(0, 3)

(0, -3)

3. The set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix) is called a .

4. For a parabola with the equation x² = 4py, the vertex is at the .

5. Find the vertex, focus, and directrix of the parabola (y - 2)² = 8(x + 1). Then sketch the graph on the coordinate plane below.

Vertex:

Focus:

Directrix:

6. The axis of symmetry for a parabola with the equation x = ay² + by + c is a horizontal line.

True

False

7. A parabolic arch has a span of 40 feet and a maximum height of 15 feet. Find the equation of the parabola.

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