# How do you write the vertex form equation of the parabola  y = x^2 - 4x + 12?

May 4, 2017

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

#### Explanation:

$y = \left\{{x}^{2} - 2 \cdot 2 x + {\left(2\right)}^{2}\right\} - {\left(2\right)}^{2} + 12$
Changing it to $\left({a}^{2} + 2 a b + {b}^{2}\right)$ form to convert it to ${\left(a + b\right)}^{2}$
$y = {\left(x - 2\right)}^{2} - 4 + 12$
$y = {\left(x - 2\right)}^{2} + 8$ is the vertex form.

May 4, 2017

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

#### Explanation:

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

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

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

As in an equation of the vertex form $y - k = a {\left(x - h\right)}^{2}$ or $y = {\left(x - h\right)}^{2} + k$ the vertex is $\left(h , k\right)$

here we have vertex at $\left(2 , 8\right)$ and vertex form of equation is $y - 8 = {\left(x - 2\right)}^{2}$

graph{x^2-4x+12 [-8.24, 11.76, 6.08, 16.08]}