SOLUTION: Find local maximal or local minimal for the function -2x^2+4x-1

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Question 887546: Find local maximal or local minimal for the function -2x^2+4x-1
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two ways to solve. One way, find the zeros and take the x value in the exact middle, and calculate the function value. The other way, complete the square to put the function into standard form and read the vertex directly from the function in its standard form. WHICH do you prefer?

x=%28-4%2B-+sqrt%2816-4%28-2%29%28-1%29%29%29%2F%282%28-2%29%29
x=%28-4%2B-+sqrt%288%29%29%2F%28-4%29
x=%28-4%2B-+2sqrt%282%29%29%2F%28-4%29
x=1%2B-+%281%2F2%29sqrt%282%29

The x in the exact middle is highlight%281%2F2%29; NOW, what is the value of the function at x=1%2F2?

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Find local maximal or local minimal for the function -2x^2+4x-1


Since "a" < 0, this PARABOLA will open DOWNWARDS, and will therefore have a MAXIMA.



f%28x%29+=+-+2x%5E2+%2B+4x+-+1

The x-coordinate of the vertex (or h) will be at x+=+-+b%2F2a

The x-coordinate of the vertex (or h) will be at x+=+-+4%2F%282%2A-+2%29, or at x+=+%28-+4%29%2F+-+4, or at x = 1

f%28x%29_or_y+=+-+2%281%29%5E2+%2B+4%281%29+-+1 ------ Substituting 1 for x 

f(x) or y = - 2 + 4 - 1

f(x) or y or k = 1  

Thus, the PARABOLA has a MAXIMA at (highlight_green%28highlight_green%281%29%29, highlight_green%28highlight_green%281%29%29)