What is the vertex of #y= -3x^2 + 12x +6 #?

1 Answer
Narad T.
Oct 16, 2016

The vertex is #(2,18)#

Explanation:

#y=-3x^2+12x+6#
Differentiating with respect to x
#dy/dx=-6x+12#
Any max or min is when #dy/dx=0#
#-6x+12=0 => 6x=12 => x=2#
To determine if it's a max or min , we must differentiate once more
So #(d^2y)/(dx^2)=-6# (<0)
so it's a maximum
The vertex is when #x=2# and #y=-3*2*2+12*2+6 =-12+24+6=18#
Here is a graph of the function

graph{-3x^2+12x+6 [-40, 40, -20, 20]}

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