SOLUTION: Find a formula for the polynomial f(x) of least degree that passes through the points (-4,0) , (5,0), and (0,-9).

(-4,0) , (5,0), and (0,-9)

Since the y-coordinate of the first two points are 0,
-4 and 5 are zeros, then f(-4)=0 and f(5)=0

So f(x) has factors (x+4) and (x-5)

So we know the polynomial f(x) is of the form 

f(x) = k(x+4)(x-5)  for some value k

We know that f(0) = -9

So

f(0) = k(0+4)(0-5) = k(4)(-5) = -20k = -9

                                   k = 

So f(x) = (x+4)(x-5)

Edwin