# What is the y coordinate of the vertex of a parabola y=x^2-4x+12?

Apr 12, 2015

Vertex is $\left(2 , 8\right)$

Method
Arrange the equation in the form $y - k = 4 a {\left(x - h\right)}^{2}$

where $\left(h , k\right)$ is your vertex.

So we have,

$\implies y = {x}^{2} - 4 x + 12$

$\implies y = {x}^{2} - 4 x + {\left(- \frac{4}{2}\right)}^{2} - {\left(- \frac{4}{2}\right)}^{2} + 12$

$\implies y = {\left(x - 2\right)}^{2} - 4 + 12$

$\implies y - 8 = {\left(x - 2\right)}^{2}$

So we get our vertex to be $\left(2 , 8\right)$