# What is the the vertex of y = -x^2 + 2x +4?

Jul 8, 2017

$\left(1 , 5\right)$

#### Explanation:

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

"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)

$y = - {x}^{2} + 2 x + 4 \text{ is in standard form }$

$\text{with } a = - 1 , b = 2 , c = 4$

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

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

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = - 1 + 2 + 4 = 5$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(1 , 5\right)$
graph{-x^2+2x+4 [-10, 10, -5, 5]}