Question

the graph of a quadratic function has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Determine an expression for the function.

Answer 1

first of all the function has to be
y = a(x+1)(x-3) but we don't know what a is

the axis of symmetry and thus the vertix is midway between the x-intercepts.
So from your information the vertex is (1,4)
then
4 = a(1+1)(1-3)
a = -1

so y = -(x+1)(x-3) or y = -x^2 + 2x + 3