# What is the vertex of y= x^2 - 8x + 18 ?

May 8, 2018

$\text{vertex } = \left(4 , 2\right)$

#### Explanation:

$\text{given a quadratic in "color(blue)"standard form}$

•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)

$y = {x}^{2} - 8 x + 18 \text{ is in standard form}$

$\text{with "a=1,b=-8" and } c = 18$

$\Rightarrow {x}_{\text{vertex}} = - \frac{- 8}{2} = 4$

$\text{substitute into the equation for y-coordinate}$

${y}_{\text{vertex}} = {4}^{2} - \left(8 \times 4\right) + 18 = 2$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(4 , 2\right)$
graph{x^2-8x+18 [-10, 10, -5, 5]}