Conic sections
Writing equations of parabolas worksheets
Write exact vertical or horizontal vertex-form equations from foci, directrices, intercepts, points or three-point interpolation.
Preview and downloadConic sections practice
Properties of parabolas worksheets
Find exact vertices, axes, openings, extrema, latus rectum lengths and coordinate intercepts from vertical and horizontal parabola equations.
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Identify the requested exact properties of each parabola.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
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Read exact features in either orientation
Each worksheet contains six parabolas in vertex or expanded form. Choose any nonempty set of extrema, latus rectum lengths, coordinate intercepts, vertices, axes and opening directions.
The x-intercepts always come from y = 0 and the y-intercepts from x = 0, including for horizontal parabolas.
The separate key supplies only the selected exact properties.
Learning objective
What this activity builds
Derive exact geometric and coordinate properties from one vertex-form or expanded parabola model.
Worked example
Find the focus and directrix of y = (x − 2)² − 3.
Focus (2, −11/4), directrix y = −13/4.
Here a = 1, so p = 1/(4a) = 1/4. Move p from the vertex toward the focus and the same distance oppositely to the directrix.
Teaching notes
Make the practice count
- Identify whether x or y is squared to determine orientation.
- Use p = 1/(4a) with its sign.
- Keep intercept roots exact.
- For horizontal parabolas, the minimum or maximum bounds x.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more exact properties, then change the seed for six reproducible vertical and horizontal parabolas.
Enlarged pages scroll. PDF size stays the same.
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