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# What is the minimum (extrema) of this equation?

I need to know the extrema value for the following equation, preferably by solving it with completing the square.        f(x)=2x2-32x+74

### 2 Answers by Expert Tutors

Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
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First, 2 can be factored out, it does not change the extrema positions.

2*(x2-16x+37); Let us from now operate on the trinomial inside the parentheses.

x2-16x+37=x2-2*8*x+82-82+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;
Justin L. | A Personalized Approach to a Standardized EducationA Personalized Approach to a Standardize...
5.0 5.0 (7 lesson ratings) (7)
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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