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.
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) = .
