How do you write the expression in the form #a(x+b)^2 +c#?

2 Answers
Nghi N
Aug 1, 2017

#f(x) = 3(x + 3)^2 - 33#

Explanation:

#f(x) = 3x^2 + 18x - 6#
First, find the coordinates of the vertex.
x-coordinate of vertex:
#x = -b/(2a) = - 18/6 = - 3#
y-coordinate of vertex:
#f(-3) = 3(9) - 18(3) - 6 = -27 - 6 = -33#
vertex form:
#f(x) = 3(x + 3)^2 - 33#

EZ as pi
Aug 1, 2017

#3(x+3)^2 -33#

Explanation:

You can apply the process of completing the square:

Make #a=1#

#3x^2+18x-6#

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

#=3[x^2 +6x color(magenta)(+(-6/2)^2) color(magenta)(-(-6/2)^2) -2]#

#=3[x^2 +6x color(magenta)(+(9) color(magenta)(-9)) -2]#

#=3[(x+3)^2 -11]#

#=3(x+3)^2 -33#

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