Question

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

Answer 1

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.

Answer 2

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.