Question

What are the coordinates of the vertex of y = x^2 - 4x - 5?

Answer 1

`y=x^2-4x-5`
is a parabola with a slope (for arbitrary values of `x`) given by the expression
`(dy)/(dx) = 2x -4`

This slope is equal to `0` at the vertex of the parabola
`2x-4 = 0`
`rarr x=2`

When `x=2` the equation for the parabola gives us
`y = (2)^2 -4*(2) -5`

`= -9`

So the coordinates of the vertex of the parabola are
`(2,-9)`