Question

Find a formula for the polynomial f(x) of least degree that passes through the points (−2,0), (2,0), and (0,−11).

Answer 1

Since the y-coordinate of the first two point are 0, and -2 and 2 are zeros, then f(-2)=0 and f(2)=0
so f(x) has factors (x+2) and (x-2)
The polynomial f(x) is of the form f(x)=k(x+2)(x-2)
But f(0)=-9
so
f(0)=k(0+2)(0-2)=-9
-4k=-9
k=9/4
hence:
f(x)=9/4(x+2)(x-2)