# How do you write y= -4x^2+8x-1 into vertex form?

May 23, 2015

General vertex form for a parabolic equation is
$y = m {\left(x - a\right)}^{2} + b$
where the vertex is at $\left(a , b\right)$

Given $y = - 4 {x}^{2} + 8 x - 1$

Extract $m$
$y = \left(- 4\right) \left({x}^{2} - 2 x\right) - 1$

Complete the square
$y = \textcolor{b l u e}{\left(- 4\right)} \left({x}^{2} - 2 x \textcolor{b l u e}{+ 1}\right) - 1 \textcolor{b l u e}{+ 4}$

$y = \left(- 4\right) \left(x - 1\right) + 3$
is in vertex form (with the vertex at $\left(1 , 3\right)$)