# What is the axis of symmetry and vertex for the graph y=-2x^2 +4x +2 ?

Jul 24, 2017

Axis of symmetry is $x - 1 = 0$ and vertex is $\left(1 , 4\right)$

#### Explanation:

To find axis of symmetry and vertex, weshould convert the equation to its vertex form $y = a {\left(x - h\right)}^{2} + k$, where $x - h = 0$ isaxis of symmetry and $\left(h , k\right)$ is the vertex.

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

$= - 2 \left({x}^{2} - 2 x\right) + 2$

$= - 2 \left({x}^{2} - 2 x + 1\right) + 2 + 2$

$= - 2 {\left(x - 1\right)}^{2} + 4$

Hence axis of symmetry is $x - 1 = 0$ and vertex is $\left(1 , 4\right)$

graph{(y+2x^2-4x-2)(x-1)((x-1)^2+(y-4)^2-0.02)=0 [-10, 10, -5, 5]}