Question

What is the vertex of `y=x^2+4x - 5`?

Answer 1

vertex at `(-2,-9)`

Explanation:

Often the simplest way to do this is to convert the given equation into "vertex form":
`color(white)("XXX")y=(x-a)^2+b` with its vertex at `(a,b)`

Given
`color(white)("XXX")y=x^2+4x-5`

Completing the square:
`color(white)("XXX")y=x^2+4xcolor(blue)(+4)-5color(blue)(-4)`

Re-writing as a squared binomial and simplified constant
`color(white)("XXX")y=(x+2)^2-9`

Modifying signs into explicit vertex form:
`color(white)("XXX")y=(x-(-2))^2+(-9)`

If you have access to some graphing software, it can help verify that the answer is reasonable by graphing the original equation.
graph{x^2+4x-5 [-8.91, 11.09, -9.59, 0.41]}