SOLUTION: f(x) = −x^2 + 8x + 3 find the maximum value of the function

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Question 1003347: f(x) = −x^2 + 8x + 3
find the maximum value of the function
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = −x^2 + 8x + 3
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max occurs at x = -b/(2a) = -8/(-2) = 4
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max value y = f(4) = -16+32+3 = 16+3 = 19
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+-x%5E2+%2B+8x+%2B+3
the maximum value of the function will be y coordinate of vertex; so, write equation in vertex form f%28x%29+=+a%28x-h%29%5E2+%2B+k
f%28x%29+=+-%28x%5E2+-8x%29+%2B+3...........complete square
f%28x%29+=+-1%2A%28x%5E2+-8x%2Bb%5E2%29-%28-1%29b%5E2+%2B+3
f%28x%29+=+-%28x%5E2+-8x%2B4%5E2%29%2B1%2A4%5E2+%2B+3
f%28x%29+=+-%28x+-4%29%5E2%2B16+%2B+3
f%28x%29+=+-%28x+-4%29%5E2%2B19
so, h=4 and k=19,vertex is at (4, 19)
=>the maximum value of the function will be y=19