SOLUTION: What is the quadratic function whose roots are 8 and -4 and whose minimum is -6?

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Question 366959: What is the quadratic function whose roots are 8 and -4 and whose minimum is -6?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=a%28x-8%29%28x%2B4%29
f%28x%29=a%28x%5E2-4x-32%29
Convert to vertex form,
f%28x%29=a%28x%5E2-4x%29-32a
f%28x%29=a%28x%5E2-4x%2B4%29-32a-4a
f%28x%29=a%28x-2%29%5E2-36a
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-36a=-6
a=1%2F6
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f%28x%29=a%28x%5E2-4x-32%29
f%28x%29=%281%2F6%29%28x%5E2-4x-32%29
highlight%28f%28x%29=+%281%2F6%29x%5E2-%282%2F3%29x-%2816%2F3%29%29+
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