# How do I convert f (x) = -2x^2 + 2x + 4 to standard form ?

## I understand how to complete the square, but this leaves me with (-2x + 4) (x+1). I thought I needed to have a perfect square ?

Nov 26, 2016

$\left(y - \frac{9}{2}\right) = - 2 {\left(x - \frac{1}{2}\right)}^{2}$

#### Explanation:

Given f(x)= y= $- 2 {x}^{2} + 2 x + 4$

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

=$- 2 \left({x}^{2} - x + \frac{1}{4} - \frac{1}{4}\right) + 4$

= $- 2 \left({x}^{2} - x + \frac{1}{4}\right) + \frac{1}{2} + 4$

=$- 2 {\left(x - \frac{1}{2}\right)}^{2} + \frac{9}{2}$

$y - \frac{9}{2} = - 2 {\left(x - \frac{1}{2}\right)}^{2}$, which is required standard form.