SOLUTION: What is the maximum value of f to four decimal places graphically, f(x)=100x-11x^2+2?

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Question 874670: What is the maximum value of f to four decimal places graphically, f(x)=100x-11x^2+2?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A formula would be nice. Try starting with general form completely in symbols, complete the square and put into standard form. You can then read the vertex directly from the equation. The constant term will be the maximum value.

f%28x%29=ax%5E2%2Bbx%2Bc, and understand that your "a" value will be negative, since as you see, in your function, a=-11.
a%28x%5E2%2Bbx%2Bc%2Fa%29
a%28x%5E2%2Bbx%2B%28b%2F2%29%5E2%2Bc%2Fa-%28b%2F2%29%5E2%29
a%28x%2Bb%2F2%29%5E2%2Bc-a%28b%2F2%29%5E2
a%28x%2Bb%2F2%29%5E2%2B4c%2F4-ab%5E2%2F4
a%28x%2Bb%2F2%29%5E2%2B%284c-ab%5E2%29%2F4
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If no mistakes were made, then maximum value is highlight%28%284c-ab%5E2%29%2F4%29; this should give your maximum f to be %284%2A2%2B11%2A100%5E2%29%2F4=110008%2F4=highlight%2827502%29

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

What is the maximum value of f to four decimal places graphically, f(x)=100x-11x^2+2?


Maximum value of f(x), or y occurs at x+=+-b%2F2a, with:

a being - 11

b being 100

x+=+-+b%2F2a ----- x+=+-+%28100%29%2F2%28-+11%29 ------ x+=+4.545454545

With x being 4.5454545454, f(x) = 100x+-+11x%5E2+%2B+2 becomes:

f(x) = 100%284.54%29+-+11%284.54%29%5E2+%2B+2

highlight_green%28f%28x%29+=+229.2724%29

You should be able to graph the parabola based on the coordinates of the vertex being (4.54, 229.2724)