Question

What is the axis of symmetry and vertex for the graph `y =-2x^2-3x+4`?

Answer 1

Axis of symmetry: `x=-3/4`
Vertex at `(-3/4, 41/8)`

Explanation:

Solution is by Completing the Square

`y=-2x^2-3x+4`

`y=-2(x^2+3/2x)+4`

`y=-2(x^2+3/2x+9/16-9/16)+4`

`y=-2((x+3/4)^2-9/16)+4`

`y=-2(x+3/4)^2+9/8+4`

`y-41/8=-2(x+3/4)^2`

`-1/2(y-41/8)=(x--3/4)^2`

Axis of symmetry: `x=-3/4`
Vertex at `(-3/4, 41/8)`

graph{y=-2x^2-3x+4[-20,20,-10,10]}

God bless....I hope the explanation is useful.