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.

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  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)
    4 = a(1+1)(1-3)
    a = -1

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

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