Question 1012046
Note that if f(-3/2)=8 is the maximum value, this is the vertex, and that if a parabola has a maximum value, the function will always be decreasing and as such, a is certainly negative.


Write this in vertex form. {{{f(x)=a(x+3/2)^2+8}}}
Expand this. {{{ax^2+a3x+a9/4+8}}}
The only way for the middle term to be -12x is for the coefficient, the a3 part of it is to equal 12 itself. So, 3a=-12, a=-4.


If a=-4, then a(9/4)=-4(9/4)=-9. Combine like terms, -9+8=-1.


{{{a=-4}}}
{{{c=-1}}}