Question

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

Answer 1

the axis of symmetry is x=-1
and the vertex is (-1,-4)

Explanation:

`y=x^2+2x-3`
Rewrite the equation in the vertex form
`y=x^2+2x+1-4=(x+1)^2-4`
The line of symmetry is when`(x+1=0)`
And the vertex is on that line`(-1,-4)`

If you have not yet studied calculus, forget what I write under

Differentiating with respect to x
`dy/dx=2x+2`
The vertex is when `dy/dx=0`
`2x+2=0=>x=-1` and `y=(-1)^2+(2*-1)-3=1-5=-4`
Differentiating once more
`(d^2y)/dx^2=2 (>0)` so we have a minimum

Here is a graph of the function
graph{x^2+2x-3 [-10, 10, -5, 5]}