# What is the vertex form of y=2x^2-18x+4 ?

Feb 15, 2017

$y = 2 {\left(x - \frac{9}{2}\right)}^{2} - \frac{73}{2}$

#### Explanation:

$y = 2 \left({x}^{2} - 9 x\right) + 4$

$= 2 \left({x}^{2} - 9 x + \frac{81}{4} - \frac{81}{4}\right) + 4$

$= 2 \left({x}^{2} - 9 x + \frac{81}{4}\right) - \frac{81}{2} + 4$

$= 2 {\left(x - \frac{9}{2}\right)}^{2} - \frac{73}{2}$, which is the required form.