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Vertex Form of a Parabola Calculator
Convert y = ax2 + bx + c into vertex form and find the vertex, axis and roots.
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Vertex form
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Convert y = ax2 + bx + c into vertex form and find the vertex, axis and roots.
Vertex Form of a Parabola Estimator
Enter your numbers below for an instant estimate.
0
💡 Tip: h = -b / (2a); k = c – b² / (4a); y = a(x – h)² + k.
How It Works
Key concepts behind this calculator
1
Enter Values
Fill in each field with your own numbers.
2
Calculate
Results update as you change the inputs.
3
Review
Read the breakdown and the explanation.
4
Adjust
Change values to compare scenarios.
Quick Reference Guide
Vertex Quick Guide
Typical values for reference.
| a | b | c | Vertex |
|---|---|---|---|
| 1 | -6 | 5 | (3.00, -4.00) |
| 1 | 0 | -4 | (0.00, -4.00) |
| -2 | 8 | 0 | (2.00, 8.00) |
| 0.5 | 2 | 1 | (-2.00, -1.00) |
| Rule of Thumb | Check inputs | Use as a guide | Round sensibly |
Common Questions
Vertex Form of Calculator FAQ
Answers to common questions about this calculator.
y = a(x – h)² + k, which shows the vertex (h, k).
h = -b / 2a.
Upward when positive, downward when negative.
Use the quadratic formula.