Converting Quadratic Equations from Vertex Form to Standard Form

Quadratic equations are equations involving squared numbers (y = x2 is the parent function). This page will show how to convert quadratic equations in vertex form into standard form easily.

Vertex Form
Quadratic equations in vertex form follow this formula:
 * y = a(x - h)2 + k

The vertex of the resulting graph is (h, k).

Standard Form
Quadratic equations in standard form follow this formula:
 * y = ax2 + bx + c

Conversion
You can convert quadratic equations by doing the following (let's use y=(x-2)2+3 for this):
 * (x - 2)2 + 3
 * (x - 2)(x - 2) + 3
 * x2 - 2x - 2x + 4 + 3
 * x2 - 4x + 7

First, the equation is expanded to remove the exponent. Then, the x's and the -2's are distributed to remove the parentheses, bringing back the exponent to only include the first x. Afterward, the equation is simplified.

If you want to save time and do it an easier way, b and c can be calculated with the following formulae:
 * b = 2h
 * c = h2 + k

Example
For y = (x + 3)2 - 5:
 * b = 2(3) = 6
 * c = 32 - 5 = 4
 * (x + 3)2 - 5 = x2 + 6x + 4