What is the the vertex of #y=(x -4)^2 + 12x -36#?

1 Answer
Shwetank Mauria
Mar 21, 2017

#y=(x-2)^2-24# is the equation in vertex form.

Explanation:

Vertex form of equation is of the type #y=a(x-h)^2+k#, where #(h,k)# is the vertex and axis of symmetry is #x-h=0#
Here we have

#y=(x-4)^2+12x-36#

#=x^2-8x+16+12x-36#

#=x^2+4x-20#

#=x^2+2xx2x+2^2-4-20#

#=(x-2)^2-24#

Hence, #y=(x-2)^2-24# is the equation in vertex form. Vertex is #(2,-24)# and axis of symmetry is #x-2=0#
graph{(x-2)^2-24-y=0 [-10, 10, -30, 10]}

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