Question

How do I use the vertex formula to determine the vertex of the graph for `y=5-8x-x^2`?

Answer 1

Put it in standard order:

`y=-x^2-8x+5` so we can see that `a=-1` and `b=-8`

The vertex has `x`-coordinate `-b/(2a)`. In this case we get:

The vertex has `x`-coordinate `-(-8)/(2(-1)) = -(-8)/(-2)=-8/2 =-4`

Knowing the `x`-coordinate of the vertex, we use the equation to find the `y`-coordinate of the vertex:

`y=-(-4)^2-8(-4)+5`

`y=-16+32+5=16+5=21`

The vertex is `(-4, 21)`