What is the vertex form of # y= (9x-6)(3x+12)-7x^2+5x#?

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Answer 1 · 2017-10-09T19:25:32

#y = 20(x-(-19/8))^2-2957/16#

Given: #y= (9x-6)(3x+12)-7x^2+5x#

Perform the multiplication:

#y =27x^2 + 90x - 72 -7x^2+5x#

Combine like terms:

#y =20x^2 + 95x - 72#

This is in the standard Cartesian form:

#y = ax^2+bx+c#

where #a = 20, b = 95, and c = -72#

The general vertex form for a parabola of this type is:

#y = a(x-h)^2+k#

We know that #a = 20#:

#y = 20(x-h)^2+k#

We know that #h = -b/(2a)#

#h = -95/(2(20))#

#h = -19/8#

#y = 20(x-(-19/8))^2+k#

We know that:

#k = 20(-19/8)^2+95(-19/8)-72#

#k = -2957/16#

#y = 20(x-(-19/8))^2-2957/16#