A technique used to rewrite a quadratic function in standard form to vertex form.

Step-by-step explanation:

A quadratic function, f (x) = ax^2 + bx + c, can be converted to vertex form, f (x) = a (x - h) ^2 + k as follows:

f (x) = ax^2 + bx + c

= a (x^2 + (b/a) x) + c

= a (x^2 + 2 (b/2a) x + (b/2a) ^2 - (b/2a) ^2) + c

= a (x^2 2 (b/2a) x + (b/2a) ^2) - a (b/2a) ^2 + c

= a (x + (b/2a)) ^2 + (c - b^2/4a)

= a (x - h) ^2 + k

where h = - b/2a and k = c - b^2/4a

The technique used is by completing the square.

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a (x - h) 2 + k, you use the process of completing the square.