# How do you write  y = -16x^2+40x+4 into vertex form?

May 7, 2015

Vertex form for a parabola is
$y = m {\left(x - a\right)}^{2} + b$
with the vertex at $\left(a , b\right)$

Re-arranging $y = 16 {x}^{2} + 40 x + 4$ into vertex form:

$y = - 16 \left({x}^{2} - \frac{5}{2} x\right) + 4 \text{ extract the "m" factor}$

$y = - 16 \left({x}^{2} - \frac{5}{2} x + {\left(\frac{5}{4}\right)}^{2}\right) + 25 + 4 \text{ complete the square}$

$y = - 16 {\left(x - \frac{5}{4}\right)}^{2} + 29$