# How do you rewrite the following quadratic equation in vertex form: y=x^2-8x+13?

Mar 20, 2017

minimum vertex with value$- 3$ at $\left(4 , - 3\right)$

#### Explanation:

$y = {x}^{2} - 8 x + 13$

Consider coefficient of $x$, divide by 2 and make a parentesis and ssquare them. since infront of parentesis is +ve value, then deduct the squared number in parentesis in the equation to balance it.
$y = {\left(x - 4\right)}^{2} - {\left(- 4\right)}^{2} + 13$
$y = {\left(x - 4\right)}^{2} - 16 + 13$
$y = {\left(x - 4\right)}^{2} - 3$

since infront of ${\left(x - 4\right)}^{2}$ is +ve sign, it is a minimum vertex with value$- 3$ at $\left(4 , - 3\right)$