Question 1189255: Find k so that the minimum value of f(x) = x^2 + kx + 8 is equal to the maximum value of g(x) = 1 + 4x -2x^2 Found 2 solutions by ikleyn, Solver92311:Answer by ikleyn(52787) (Show Source):
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Find k so that the minimum value of f(x) = x^2 + kx + 8 is equal to the maximum value of g(x) = 1 + 4x -2x^2
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Solve it in three steps.
STEP 1. Find the maximum value of g(x) = 1 + 4x - 2x^2 .
Find = " -b/(2a) " = = = 1.
Then = 1 + 4*1 - 2*1^2 = 1 + 4 - 2 = 3.
STEP 2. Find the minimum value of f(x) = x^2 + kx +8 .
= - + 8.
The minimum value of f(x) is = - +
STEP 3. Find k .
We will find the value of k from this equation
= ,
which is
3 = - + .
Simplify and find k
12 = + 32
= 32 - 12
= 20
k = +/- .
ANSWER. There are two values for k: = and - = -.
