posted by kelly .
find a possible polynomial equation of degree 4 if the zeroes are -1,2, and 5, the graph touches the x-axis at -1 but does not cross through, and the y intercept is -5
there must be double root at x = -1
so it must be
y = a(x-2)(x-5)(x+1)^2
also we know (0,-5) lies on it, so
-5 = (-2)(-5)(1)
-5 = 10a
a = -1/2
with your information there is a unique polynomial of
y = (-1/2)(x-2)(x-5)(x+1)^2
expand if need be.