2011/085) The quadratic function f(x) is negative for x > 9/2 and x < -1, but for no other value of x. If f(1) = 28 find f(x)

As it is –ve for x > 9/2 and x < -1 it is of the form –A (x-9/2)(x+1) where A > 0

Or – B(2x-9)(x+1)(where B = A/2)

F(1) = -B(-7)(2) = 28A = 28 or B = 2

So we get

F(x) = – 2(2x-9)(x+1)