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Conic sections practice

Writing equations of parabolas worksheets

Write exact vertical or horizontal vertex-form equations from foci, directrices, intercepts, points or three-point interpolation.

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Use the given information to write each parabola in vertex form.

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Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
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Build vertex form from exact givens

Each worksheet contains ten constructions selected from nine actual forms, including focus/directrix relationships, a vertex and point, and three-point interpolation.

Find the signed focal parameter or solve the printed coordinate conditions, then write the correct vertical or horizontal vertex form.

The separate key derives one exact equation from the supplied givens.

Learning objective

What this activity builds

Use exact geometric or coordinate givens to determine one parabola in vertex form.

Worked example

Write the vertical parabola with vertex (2, −1) and focus (2, 1).

y = (1/8)(x − 2)² − 1.

The signed focal parameter is p = 2, so a = 1/(4p) = 1/8.

Teaching notes

Make the practice count

  • Find the vertex and signed focal distance before calculating a.
  • For a vertex and point, substitute the point into vertex form.
  • Three-point prompts require interpolation; they do not supply a hidden vertex.
  • Swap x and y roles for horizontal parabolas.

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Choose your options, update the preview, then download the exact same pages.

Choose one or more given forms, then change the seed for ten reproducible parabola equations.

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Math SheetNameScore/ 10TeacherDateWriting Equations of ParabolasUse the given information to write each parabola in vertex form.1.Vertex:(0,0)Focus:(0,-112)Vertex-form equation:2.Vertex:(1,-1)Focus:(1,-78)Vertex-form equation:3.Vertex:(0,0)Directrix:y=116Vertex-form equation:4.Vertex:(-2,-4)Directrix:y=-6516Vertex-form equation:5.Opens:up/downVertex:(4,-6)y-intercept:(0,74)Vertex-form equation:6.Focus:(-7,-134)Directrix:y=-114Vertex-form equation:math-sheet.comPage 1 / 2
Math SheetNameScore/ 10TeacherDateWriting Equations of ParabolasUse the given information to write each parabola in vertex form.7.Opens:left/rightVertex:(-3,8)Point:(-35,12)Vertex-form equation:8.Three points (opens up/down):(-3,-28),(1,-4),(4,-49)Vertex-form equation:9.Vertex:(0,0)Opens:rightFocal distance:14Vertex-form equation:10.Vertex:(0,0)Focus:(0,-120)Vertex-form equation:math-sheet.comPage 2 / 2

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