# What is the vertex form of y= x^2-x-56 ?

Jul 6, 2017

 y=(x-1/2)^2-225/4

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$\text{for a parabola in standard form } y = a {x}^{2} + b x + c$

$\text{the x-coordinate of the vertex is }$

${x}_{\textcolor{red}{\text{vertex}}} = - \frac{b}{2 a}$

$y = {x}^{2} - x - 56 \text{ is in standard form}$

$\text{with } a = 1 , b = - 1 , c = - 56$

.>$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 1}{2} = \frac{1}{2}$

$\text{substitute into function for y-coordinate of vertex}$

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = {\left(\frac{1}{2}\right)}^{2} - \frac{1}{2} - 56 = - \frac{225}{4}$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex}} = \left(\frac{1}{2} , - \frac{225}{4}\right)$

$\Rightarrow y = {\left(x - \frac{1}{2}\right)}^{2} - \frac{225}{4} \leftarrow \textcolor{red}{\text{ in vertex form}}$