SOLUTION: What is the maximum and minimum of a quad equation Thanks

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Question 222: What is the maximum and minimum of a quad equation
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Answer by KMST(5483) About Me  (Show Source):
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A quadratic function of the form
y=ax%5E2%2Bbx%2Bc has a maximum if a%3C0 with x%5Bmax%5D=-b%2F%222+a%22 ,
and a minimum if a%3E0 with x%5Bmin%5D=-b%2F%222+a%22 ,
because the function can be re-written as y%22=%22a%28x%2Bb%2F%222+a%22%29%5E2%2B%284ac-b%5E2%29%2F%224+a%22 ,
where %28x%2Bb%2F%222+a%22%29%5E2%3E=0 with the minimum %28x%2Bb%2F%222+a%22%29%5E2=0 at x=-b%2F%222+a%22 .

y%22=%22ax%5E2%2Bbx%2Bc%22=%22a%28x%5E2%2B%28b%2Fa%29x%29%2Bc%22=%22a%28x%5E2%2B%28b%2Fa%29x%2Bb%5E2%2F4a%5E2-b%5E2%2F4a%5E2%29%2Bc%22=%22a%28x%5E2%2B%28b%2Fa%29x%2Bb%5E2%2F4a%5E2%29%2Ba%28-b%5E2%2F4a%5E2%29%2Bc%22=%22a%28x%2Bb%2F2a%29%5E2%2Bc-b%5E2%2F4a%22=%22a%28x%2Bb%2F2a%29%5E2%2B%284ac-b%5E2%29%2F4a