# How do you write the quadratic in vertex form given y=5x^2+5x-3?

May 2, 2015

To be in vertex form a quadratic needs to be expressed as
$y = \textcolor{red}{m} {\left(x - \textcolor{g r e e n}{a}\right)}^{2} + \textcolor{\mathmr{and} a n \ge}{b}$
(where $\left(a , b\right)$ is the vertex of the quadratic),

$y = 5 {x}^{2} + 5 x - 3$

$y = \textcolor{red}{5} \left({x}^{2} + x\right) - 3 \text{ extract the "color(red)( m)" term}$

y = color(red)(5)(color(blue)(x^2+x+(1/2)^2) -(1/2)^2)-3 " "color(blue)("complete the square")

$y = \textcolor{red}{5} {\left(x + \frac{1}{2}\right)}^{2} - \frac{5}{4} - 3$

$y = \textcolor{red}{5} {\left(x - \textcolor{g r e e n}{\left(- \frac{1}{2}\right)}\right)}^{2} + \textcolor{\mathmr{and} a n \ge}{\left(- 4 \frac{1}{4}\right)}$