SOLUTION: If f(x)=ax^2-12x+c and f(-3/2)=8 is the maximum value, find the values of a and c.

Question 1012046: If f(x)=ax^2-12x+c and f(-3/2)=8 is the maximum value, find the values of a and c.
Found 2 solutions by ValorousDawn, stanbon:
Answer by ValorousDawn(53) (Show Source): You can put this solution on YOUR website!
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.
Expand this.
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.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If f(x)=ax^2-12x+c and f(-3/2)=8 is the maximum value,
find the values of a and c.
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Max occurs at x = -b/(2a)
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Therefore:: -b/(2a) = -3/2
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b = -12
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12/(2a) = -3/2
-6a = 24
a = -4
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Using (-3/2,8), solve for "c"::
-4(-3/2)^2 - 12(-3/2) + c = 8
----
-9 + 18 + c = 8
c = -1
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Cheers,
Stan H.
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