Question 1052724
The function is y=-3x^2+12x-9
The derivative is -6x+12
set that equal to 0
-6x+12=0
6x=12
x=2
At x=2 the function has a rate of instantaneous change of 0.
It is positive, so this is a local maximum.
The value of y is 3
The vertex x-value is at -b/2a or -12/-6=2 as a check
f(2)=-12+24-9=3.
{{{graph(300,300,-10,10,-10,10,-3x^2+12x-9)}}}