Grade 10 Vertex Form Worksheets
Start with eight focused practice problems, then use the answer key below to check the worksheet.
Practice Worksheet
Grade 10 Vertex Form 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 use vertex form to connect algebraic equations with transformations and key features of quadratic graphs.
Vertex form worksheets focus on quadratics written as y = a(x - h)^2 + k, where the vertex is (h, k). Grade 10 students use this form to identify the maximum or minimum point of a parabola quickly, describe transformations, and sketch graphs without building a full table of values.
These worksheets ask students to read the vertex, axis of symmetry, direction of opening, and vertical stretch from an equation. They also practise converting from standard form to vertex form by completing the square and interpreting vertex form in word problems such as projectile motion or area optimization. Vertex form is useful because it makes the graph's key feature visible. Students who understand it can choose the best quadratic form for the question instead of treating every equation the same way.
Skills Practised
- Identifying the vertex from y = a(x - h)^2 + k
- Finding the axis of symmetry
- Describing transformations of a parabola
- Sketching a quadratic from vertex form
- Converting standard form to vertex form
Parent Tip: The answer key can confirm the vertex and equation, but the sign inside the brackets is easy to miss. Ask your teen to label h and k, or use photo checking for the conversion steps.