Question

What is the axis of symmetry and vertex for the graph `y = -2x^2 + 10x - 1`?

Answer 1

Axis of symmetry is `x-5/2=0` and vertex is `(5/2,23/2)`

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+10x-1`

`=-2(x^2-5x)-1`

`=-2(x^2-2xx5/2xx x+(5/2)^2)+2(5/2)^2-1`

`=-2(x-5/2)^2+23/2`

Hence axis of symmetry is `x-5/2=0` and vertex is `(5/2,23/2)`

graph{(y+2x^2-10x+1)(2x-5)((x-5/2)^2+(y-23/2)^2-0.04)=0 [-19.34, 20.66, -2.16, 17.84]}