SOLUTION: The function f(x) = 2x^2 - bx + 23 has a minimum value of 5. Find the value of b.

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Question 1111590: The function f(x) = 2x^2 - bx + 23 has a minimum value of 5. Find the value of b.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
If were in y=a%28x-h%29%5E2%2Bk form, you could read the vertex as point (h,k).
Your example would indicate (h,5).

2%28x%5E2-%28b%2F2%29x%29%2B23
2%28x%5E2-%28b%2F2%29x%2Bb%5E2%2F16-b%5E2%2F16%29%2B23
2%28%28x-b%2F4%29%5E2-b%5E2%2F16%29%2B23
2%28x-b%2F4%29%5E2-b%5E2%2F8%2B23
2%28x-b%2F4%29%5E2%2B23-b%5E2%2F8

If no mistakes made, 23-b%5E2%2F8=5
-
-b%5E2%2F8=-18
b%5E2=18%2A8
b%5E2=144
highlight%28b=12%29

(or b = -12 )