# What is the vertex form of y=x^2-7x+1?

Jan 4, 2018

$y = {\left(x - \frac{7}{2}\right)}^{2} - \frac{45}{4}$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

"given the equation in standard form ";ax^2+bx+c

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

•color(white)(x)x_(color(red)"vertex")=-b/(2a)

$y = {x}^{2} - 7 x + 1 \text{ is in standard form}$

$\text{with "a=1,b=-7" and } c = 1$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 7}{2} = \frac{7}{2}$

$\text{substitute this value into the equation for y}$

${y}_{\textcolor{red}{\text{vertex}}} = {\left(\frac{7}{2}\right)}^{2} - 7 \left(\frac{7}{2}\right) + 1 = - \frac{45}{4}$

$\Rightarrow y = {\left(x - \frac{7}{2}\right)}^{2} - \frac{45}{4} \leftarrow \textcolor{red}{\text{in vertex form}}$