Grade 10 Completing the Square Worksheets
Start with eight focused practice problems, then use the answer key below to check the worksheet.
Practice Worksheet
Grade 10 Completing the Square Practice
Solve each problem. Show your work.
- 1.Rewrite in vertex form by completing the square: x^2 + 2x + 2
- 2.Rewrite in vertex form by completing the square: x^2 + 10x + 15
- 3.Rewrite in vertex form by completing the square: x^2 + 12x + 31
- 4.Rewrite in vertex form by completing the square: x^2 - 8x + 16
- 5.Rewrite in vertex form by completing the square: x^2 + 12x + 40
- 6.Rewrite in vertex form by completing the square: x^2 - 10x + 29
- 7.Rewrite in vertex form by completing the square: x^2 - 6x + 16
- 8.Rewrite in vertex form by completing the square: x^2 + 8x + 6
Show answer key
- Question 1: (x + 1)^2 + 1
- Question 2: (x + 5)^2 - 10
- Question 3: (x + 6)^2 - 5
- Question 4: (x - 4)^2
- Question 5: (x + 6)^2 + 4
- Question 6: (x - 5)^2 + 4
- Question 7: (x - 3)^2 + 7
- Question 8: (x + 4)^2 - 10
Next Steps
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About These Worksheets
Grade 10 students complete the square to analyze quadratic graphs and move between standard and vertex form.
Completing the square worksheets guide Grade 10 students through rewriting a quadratic so it reveals a perfect square. The process can feel abstract at first, but it gives students a direct path from standard form to vertex form, which identifies the vertex and axis of symmetry of a parabola. It also explains where the quadratic formula comes from.
These worksheets start with quadratics where the leading coefficient is 1, then progress to cases requiring factoring first. Students practise taking half of the x-coefficient, squaring it, adding and subtracting the same value, and rewriting the expression as a squared binomial. Completing the square strengthens algebraic precision and deepens understanding of quadratic structure, especially the relationship between equation form and graph features.
Skills Practised
- Creating a perfect square trinomial
- Rewriting quadratics in vertex form
- Finding the vertex from completed-square form
- Handling leading coefficients before completing the square
- Connecting completing the square to the quadratic formula
Parent Tip: This is a multi-step process that is easy to misread. Use the answer key for the vertex form, then rely on photo checking if your teen needs feedback on the add-and-subtract step.