SOLUTION: a) Determine what value of x gives the optimal value of the functions and b) Determine the optimal (maximum or minimum) value of the functions: 1. y = x^2 - 2x 2. y = 6 - 4x

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Question 1006648: a) Determine what value of x gives the optimal value of the functions and b) Determine the optimal (maximum or minimum) value of the functions:
1. y = x^2 - 2x
2. y = 6 - 4x - 2x^2
3.f(x)= x^2 + 2x - 3
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a) Determine what value of x gives the optimal value of the functions and b) Determine the optimal (maximum or minimum) value of the functions:
"Optimal" values for quadratics occur when x = -b/(2a)
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1. y = x^2 - 2x
x = 2/(2*1) = 1
f(1) = 1-2 = -1
Vertex:: (1,-1) is a minimum because a > 0
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2. y = 6 - 4x - 2x^2
x = 4/(2*-2) = -1
f(-1) = 6 + 4 - 2 = 8
Vertex:: (-1,8) is a maximum because a < 0
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Cheers,
Stan H.
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3.f(x)= x^2 + 2x - 3

SOLUTION: a) Determine what value of x gives the optimal value of the functions and b) Determine the optimal (maximum or minimum) value of the functions: 1. y = x^2 - 2x 2. y = 6 - 4x - 2x