Question

How do you find the vertex of `f(x)=x^2-1`?

Answer 1

Your function is a quadratic that is represented by a parabola. The vertex represents a point where the curve neither goes up nor down, i.e., where the slope is zero. This means that at that particular point the derivative will be zero; so:
derivative: `f'(x)=2x`
This derivative is equal to zero only when `x=0`.
Your vertex will then have coordinates:
`x=0`
substitute in your function to get:
`y=-1`