Question

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

Answer 1

Axis of symmetry is `x-1=0` and vertex is `(1,4)`

Explanation:

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

`y=-2x^2+4x+2`

`=-2(x^2-2x)+2`

`=-2(x^2-2x+1)+2+2`

`=-2(x-1)^2+4`

Hence axis of symmetry is `x-1=0` and vertex is `(1,4)`

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