Vertex Form Calculator

Convert vertex form a(x − h)² + k into standard form.

x² coefficient 1

x coefficient -6

constant 7

Formula: a(x − h)² + k = a·x² − 2ah·x + (ah² + k)

Step-by-step with your numbers:

1. Values used:

2. a = 1

3. h = 3

4. k = -2

6. x² coefficient = 1

7. x coefficient = a x h x k = 1 x 3 x -2 = -6

8. constant = 7

Did we solve your problem today?

Vertex form makes the parabola's turning point obvious; this expands it to standard form.

The math behind it

Expand a(x − h)² + k = a·x² − 2ah·x + (ah² + k). The vertex is at (h, k).

(x − 3)² − 2 = x² − 6x + 7.

How do I go the other way?

Complete the square to convert standard form back into vertex form.