9. A function p(x) with x intercepts of (-1,0) and (3,0) can be written as p(x) = a(x+1)(x-3), where 'a' is the leading coefficient.
10. The vertex form of the parabola is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. Since the parabola is translated 5 units down and 2 units right from the parent function f(x), its vertex is at (-2+2, 6-5) = (0,1). We can substitute (-2,6) into the equation and solve for 'a' to get the final equation.
f(x) = a(x-0)^2 + 1
6 = a(-2-0)^2 + 1
5 = 4a
a = 5/4
Therefore, the equation of the parabola in vertex form is f(x) = (5/4)(x-0)^2 + 1.
(If this doesn’t seem right to you comment!)