SOLUTION: Determine, without graphing weather the function f(x)=-x²+3x+4 has a maximum value or a minimum value and then find the value.

Algebra ->  Rational-functions -> SOLUTION: Determine, without graphing weather the function f(x)=-x²+3x+4 has a maximum value or a minimum value and then find the value.       Log On


   

Question 1046688: Determine, without graphing weather the function f(x)=-x²+3x+4 has a maximum value or a minimum value and then find the value.


Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Negative coefficient on the square or leading term. That tells you....

To FIND the value of the ,... vertex,
-%28x%5E2-3x-4%29
-%28x%2B1%29%28x-4%29


Roots are at -1 and +4.
Vertex occurs in the middle of these roots, or %28-1%2B4%29%2F2=3%2F2 and you can evaluate y on your own now.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine, without graphing weather the function f(x)=-x²+3x+4 has a maximum value or a minimum value and then find the value.
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The dominant term is -x
^2
As x gets less the less negative that term gets less
and less negative (y rises).
As x gets more and more positive that term gets
more and more negative y decreases.
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So the function rises then falls; it must have a maximum.
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Max occurs when x = -b/(2a) = -3/(2*-1) = 3/2
f(3/2) = -(3/2)^2+3(3/2)+4 = -9/4 + 18/4 + 16/4 = 25/4 = 6.25
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Cheers,
Stan H.
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