# How do you write 4x^2-12x+7 into vertex form?

May 3, 2015

In vertex form
$y = m {\left(x - a\right)}^{2} + b$
where $\left(a , b\right)$ is the vertex of the quadratic.

$y = 4 {x}^{2} - 12 x + 7$

$y = 4 \left({x}^{2} - 3 x\right) + 7 \text{ extract } m$

$y = 4 \left({x}^{2} - 3 x + {\left(\frac{3}{2}\right)}^{2}\right) - 9 + 7 \text{ complete the square}$

$y = 4 {\left(x - \frac{3}{2}\right)}^{2} - \left(- 2\right)$

and the vertex is at $\left(\frac{3}{2} , - 2\right)$