What is the vertex form of # y= (3x-8)(-6x-2)+2x^2+3x#?

1 Answer
Jun 2, 2018

Vertex #(45/32, 3049/64)#

Explanation:

#y=(3x-8)(-6x-2)+2x^2+3x#

#y=-18x^2-6x+48x+16+2x^2+3x#

#y=-16x^2+45x+16#

The vertex is found by #x=-b/(2a)#

By looking at the general formula of a quadratic function,
#y=ax^2+bx+c# , we can see that #b=45# and #a=-16#

#x=-b/(2a) = -45/(2times-16) = 45/32#

Sub #x=45/32# into #y=-16x^2+45x+16#

#y=-16(45/32)^2+45(45/32)+16#
#y= 3049/64#

Vertex #(45/32, 3049/64)#

You can from the graph below that the vertex is quite high up.

graph{(3x-8)(-6x-2)+2x^2+3x [-10, 10, -5, 5]}