SOLUTION: How do I solve this problem f(x) = -0.3x^2 + 25x + 16 using the quadratic formula and graphing...I'm lost. I know x = 1 if this helps.

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Question 258234: How do I solve this problem f(x) = -0.3x^2 + 25x + 16 using the quadratic formula and graphing...I'm lost. I know x = 1 if this helps.
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
No x does not equal 1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.3x%5E2%2B25x%2B16+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2825%29%5E2-4%2A-0.3%2A16=644.2.

Discriminant d=644.2 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-25%2B-sqrt%28+644.2+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2825%29%2Bsqrt%28+644.2+%29%29%2F2%5C-0.3+=+-0.635158878390421
x%5B2%5D+=+%28-%2825%29-sqrt%28+644.2+%29%29%2F2%5C-0.3+=+83.9684922117238

Quadratic expression -0.3x%5E2%2B25x%2B16 can be factored:
-0.3x%5E2%2B25x%2B16+=+-0.3%28x--0.635158878390421%29%2A%28x-83.9684922117238%29
Again, the answer is: -0.635158878390421, 83.9684922117238. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.3%2Ax%5E2%2B25%2Ax%2B16+%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve this problem f(x) = -0.3x^2 + 25x + 16 using the quadratic formula and graphing
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You use the quadratic formula to find roots or zeroes of the equation.
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-0.3x^2 + 25x + 16 = 0
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x = [-25 +- sqrt(25^2 - 4*-0.3*16)]/(2*-0.3)
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x = [-25 +- sqrt(625 + 19.2)]/(-0.6)
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x = [-25 + 25.3811]/(-0.6) or x = [-50.3811]/(-0.6) = 83.97
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x = 0.3811/(-0.6) = -0.6352... or x = 83.97..
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Cheers,
Stan H.