# How do I use the vertex formula to determine the vertex of the graph for y=-x^2+4x+12?

May 16, 2018

(2,16) is the maximum

#### Explanation:

$\frac{- b}{2 a}$ gives you the x coordinate at the vertex

$\frac{- 4}{2 \times - 1} = \frac{- 4}{- 2} = 2$

If x=2, $y = - {2}^{2} + 4 \times 2 + 12 \implies y = 16$

(2,16) is the vertex

May 16, 2018

The vertix $\left({x}_{v} , {y}_{v}\right) = \left(2 , 16\right)$

#### Explanation:

$y = a {x}^{2} + b x + c$

${x}_{v} = - \frac{b}{2 a}$

${y}_{v} = a {\left({x}_{v}\right)}^{2} + b \left({x}_{v}\right) + c$

$y = - {x}^{2} + 4 x + 12$

${x}_{v} = - \frac{4}{- 2} = 2$

${y}_{v} = - {\left(2\right)}^{2} + 4 \left(2\right) + 12 = - 4 + 8 + 12 = 16$

The vertix $\left({x}_{v} , {y}_{v}\right) = \left(2 , 16\right)$