# What is the vertex form of y= x^2-3x-1 ?

Oct 3, 2017

$y = {\left(x - \frac{3}{2}\right)}^{2} - \frac{13}{4}$

#### Explanation:

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

•color(white)(x)y=a(x-h)^2+k

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

$\text{given the parabola in standard form }$

•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0

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

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

$y = {x}^{2} - 3 x - 1 \text{ is in standard form}$

$\text{with } a = 1 , b = - 3 , c = - 1$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 3}{2} = \frac{3}{2}$

$\text{substitute this value into y for y-coordinate}$

${y}_{\textcolor{red}{\text{vertex}}} = {\left(\frac{3}{2}\right)}^{2} - 3 \left(\frac{3}{2}\right) - 1 = - \frac{13}{4}$

$\Rightarrow \left(h , k\right) = \left(\frac{3}{2} , - \frac{13}{4}\right)$

$\Rightarrow y = {\left(x - \frac{3}{2}\right)}^{2} - \frac{13}{4} \leftarrow \textcolor{red}{\text{ in vertex form}}$