answer
[tex]-3x^{2} +6x + 24[/tex]
explanation
since there are 2 x-intercepts, the lowest degree the function could possibly have is 2, so this could be the graph of a parabola
since our zeros are at x = 4 and x = -2, our factors are (x - 4) and (x + 2)
our equation so far is
(x - 4)(x + 2)
= [tex]x^2 -4x + 2x - 8[/tex]
= [tex]x^{2} -2x - 8[/tex]
since the function is reflected across the x-axis, multiply the equation by -1
[tex]-(x^{2} -2x - 8)[/tex]
= [tex]-x^{2} +2x + 8[/tex]
since the function has a vertical stretch of 3, multiply the equation by 3
[tex]3(-x^{2} +2x + 8)[/tex]
= [tex]-3x^{2} +6x + 24[/tex]
