Vertex Form Calculator
Convert a parabola between standard form y = ax² + bx + c and vertex form y = a(x − h)² + k.
Change the values and press Calculate to work out your own figures.
Standard form to vertex form
Enter a, b and c of y = ax² + bx + c.
Show the working
- h = −b ÷ 2a = -0.375
- k = c − b² ÷ 4a = 0.4375
Vertex form to standard form
Enter a, h and k of y = a(x − h)² + k.
Show the working
- b = −2ah = 12
- c = ah² + k = 13
How to use it
Enter a, b and c of y = ax² + bx + c. Enter a, h and k of y = a(x − h)² + k.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
h = −b ÷ 2a, k = c − b² ÷ 4a; b = −2ah, c = ah² + k
Reading the vertex
In y = a(x − h)² + k the vertex is (h, k): a minimum when a > 0, a maximum when a < 0.
Questions
Vertex form of y = 4x² + 3x + 1?
y = 4(x + 3/8)² + 7/16.
Formulas
h = −b ÷ 2a, k = c − b² ÷ 4a; b = −2ah, c = ah² + k
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).