Question

What is the the vertex of `y =(x - 16)^2 + 40x-200`?

Answer 1

vertex`-> (x,y)->(-4,40)`

Explanation:

Given: `color(white)(xxx) y=(x-16)^2+40x-200`

expand the bracket

`y=x^2 -32x+256+40x-200`

Simplify

`y=x^2+8x+56....................(1)`

Consider the +8 from `+8x`

`x_("vertex") =(-1/2)xx(+8)=color(blue)(-4.)..............(2)`

Substitute (2) into (1) giving:

`y=(color(blue)(-4))^2+8(color(blue)(-4))+56`

`y=16-32+56 =40`

So vertex`-> (x,y)->(-4,40)`