Polynomials
Completing the square worksheets
Find the missing constant in ten monic quadratic trinomials. Choose whole, fractional or mixed linear coefficients and check exact reduced answers.
Preview and downloadConic sections practice
Properties of circles worksheets
Find exact circle centers and positive radii from standard and rearranged general equations using whole numbers, fractions and radicals.
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Find the exact center and positive radius of each circle.
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Complete two squares to reveal the circle
Each worksheet contains ten circle equations. Choose whole numbers, fractions, radicals or a coherent mixture, then practice standard form, rearranged general form or five of each.
For x² + y² + Dx + Ey + F = 0, the center is (−D/2, −E/2). Substitute those exact coordinates to find radius squared, then take the positive square root.
The separate key repeats each equation, gives the exact center and radius, and shows the equivalent standard form.
Learning objective
What this activity builds
Recover a circle’s exact center and positive radius from standard form or a normalized general equation.
Worked example
Find the center and radius of x² + y² − 6x + 4y − 12 = 0.
Center (3, −2), radius 5.
Complete each square: (x − 3)² + (y + 2)² = 25.
Teaching notes
Make the practice count
- In general form, halve each linear coefficient and change its sign to find the center.
- Compute radius squared before taking the positive square root.
- Move terms carefully when the two square terms appear on different sides.
- Keep fractional and radical values exact.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more exact value types and the equation form, then change the seed for a reproducible set of ten circles.
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Simplifying square roots worksheets
Generate 10 square-root problems using perfect squares, nonperfect radicands or outside coefficients. Practice exact factor extraction with a separate answer key.
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