I need to know the extrema value for the following equation, preferably by solving it with completing the square. f(x)=2x^{2}-32x+74
What is the minimum (extrema) of this equation?
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2 Answers
First, 2 can be factored out, it does not change the extrema positions.
2*(x^{2}-16x+37); Let us from now operate on the trinomial inside the parentheses.
x2-16x+37=x^{2}-2*8*x+8^{2}-8^{2}+37=(x-8)^{2}-64+37=(x-8)^{2}-27.
This expression has a minimum when (x-8)^{2} is minimal. Since square of any number is nonnegative, the minimum is attained when (x-8)^{2}=0 or x=8. In this case f(8)=-27;
Get the x value first using the axis of Symmetry -b/2a. Once you get that x value just plug it in. The answer you get will be the min