Question

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

Answer 1

Axis of symmetry:`y=-1`
Vertex=`(-1,5)`

Explanation:

The equation is in the form `y=ax^2+bx+c`, so this can be used in finding the axis of symmetry. As we can see, the question given has values `a=2,b=4,c=3`
Axis of symmetry: `y=-b/(2a)`
`y=-4/(2(2))`
`y=-4/4`
`y=-1`

As for the vertex, you will need to complete the square in other words bring it to the form `y=a(x-h)^2-k,` from which you can get the vertex as `(h,k)`:
`y=2x^2+4x-3`
`y=2x^2+4x+2-3-2`
`y=2(x^2+2x+1)-5`
`y=2(x+1)^2-5`

From this, we see `h=-1` and `k=5`, therefore the vertex is `(-1,5)`

If any help is needed as to how I completed the square please say so