What is the the vertex of y =(x - 16)^2 + 40x-200 y=(x16)2+40x200?

1 Answer
Nov 27, 2015

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

Explanation:

Given: color(white)(xxx) y=(x-16)^2+40x-200×xy=(x16)2+40x200

expand the bracket

y=x^2 -32x+256+40x-200y=x232x+256+40x200

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)
Tony B