Completing the Square Calculator
Rewrite ax² + bx + c in vertex form a(x − h)² + k by completing the square.
Vertex form
2(x + 2)² − 5
- Standard form
- 2x² + 8x + 3
- Vertex (h, k)
- (-2, -5)
- Axis of symmetry
- x = -2
Show the work
Vertex x: h
h = −b ÷ 2a
−8 ÷ (2 × 2) = −2
Vertex y: k
k = c − b to the power of 2 ÷ 4a
3 − 8 to the power of 2 ÷ (4 × 2) = −5
Vertex form
a(x − h) to the power of 2 + k
2(x + 2)² − 5
How it works
ax² + bx + c = a(x − h)² + k with h = −b ÷ 2a and k = c − b² ÷ 4a
Questions
- How does the completing the square calculator work?
- ax² + bx + c = a(x − h)² + k with h = −b ÷ 2a and k = c − b² ÷ 4a.
- What do I need to enter?
- a, b, c. Optional fields can be left blank.
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