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

1 Answer
Tony B
Nov 27, 2015

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)#
Tony B

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