What is the vertex of #y=-2x^2 - 8x + 9#?

1 Answer
Dec 15, 2015

Vertex: #(-2,17)#

Explanation:

Our objective will be to convert the given equation into "vertex form":
#color(white)("XXX")y=m(x-a)^2+b# with vertex at #(a,b)#

Given
#color(white)("XXX")y=-2x^2-8x+9#

Extract the #m# factor
#color(white)("XXX")y=(-2)(x^2+4x)+9#

Complete the square:
#color(white)("XXX")y=(color(blue)(-2))(x^2+4xcolor(blue)(+4))+9color(red)(+8)#

Re-write the #x# expression as a binomial square
#color(white)("XXX")y=(-2)(x+2)^2+17#

Convert the squared binomial into form #(x-a)#
#color(white)("XXX")y=(-2)(x-(-2))+17#
which is the vertex form with vertex at #(-2,17)#
graph{-2x^2-8x+9 [-16.13, 15.93, 6, 22.01]}