Question

What is the vertex form of Y = x2 - 6x + 6?

Answer 1

`\large\boxed{y=(x-3)^2-3}`

Explanation:

The vertex form of a quadratic equation y = ax² + bx + c:

y = a(x - h)² + k

(h, k) - coordinates of a vertex

We have the equation y = x² - 6x + 6.

Convert to the vertex form:

`y=x^2-2(x)(3)+6\\\\y=\underbrace{x^2-2(x)(3)+3^2}_((*))-3^2+6\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\y=(x-3)^2-9+6\\\\y=(x-3)^2-3\to h=3,\ k=-3`