Question 769789
Q:
The graph of a quadratic function (a parabola) 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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A:
y = a(x - 1)(x + 3)
y = {{{a(x^2 + 2x - 3)}}}
y = {{{ax^2 + 2ax - 3a}}}
In y = {{{Ax^2 + Bx + C}}} the vertex is (h,k) where h = {{{(-B)/2A}}} and k = {{{(4AC - B^2)/4A}}}.
If A < 0, then y &#8804; k.
In y = {{{ax^2 + 2ax - 3a}}},
k = {{{(4a(-3a) - (2a)^2)/4a}}} = -4a
-4a = 4
a = -1
so the quadratic function is 
{{{highlight(y = -x^2 - 2x + 3)}}}.