SOLUTION: The quadratic function f is positive only on the intervals (−∞, 0) and (10, ∞). f has a minimum value of −100. Determine the coefficients of f.

Question 1108284: The quadratic function f is positive only on the intervals (−∞, 0) and (10, ∞). f has a minimum value of −100. Determine the coefficients of f.

Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

Since f(x) has the roots at x= 0  and  x= 10,


f(x) = k*(x-0)*(x-10) = kx*(x-10)  


at some real "k".



Since f(x) has the minimum -100,

-100 = f(5) = 5k*(5-10) = 5k*(-5) = -25k,


which implies  k =  = 4.



Thus f(x) = 4x*(x-10) = .

Solved.

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SOLUTION: The quadratic function f is positive only on the intervals (&#8722;&#8734;, 0) and (10, &#8734;). f has a minimum value of &#8722;100. Determine the coefficients of f.

SOLUTION: The quadratic function f is positive only on the intervals (−∞, 0) and (10, ∞). f has a minimum value of −100. Determine the coefficients of f.