SOLUTION: Determine whether there is a maximum or minimum value for the given function, and find that value. f(x)=-x^2+3x-5

Algebra ->  Functions -> SOLUTION: Determine whether there is a maximum or minimum value for the given function, and find that value. f(x)=-x^2+3x-5      Log On


   

Question 922855: Determine whether there is a maximum or minimum value for the given function, and find that value.
f(x)=-x^2+3x-5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Convert to vertex form by completing the square.
f%28x%29=-x%5E2%2B3x-5
f%28x%29=-%28x%5E2-3x%29-5
f%28x%29=-%28x%5E2-3x%2B9%2F4%29-5%2B9%2F4
f%28x%29=-%28x-3%2F2%29%5E2-20%2F4%2B9%2F4
f%28x%29=-%28x-3%2F2%29%5E2-11%2F4
The vertex is (3/2,-11/4).
The parabola opens downwards so the maximum value of the function is -11%2F4.
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graph%28300%2C300%2C-2%2C8%2C-8%2C2%2C-x%5E2%2B3x-5%29