Question 934652
the system of equations will be:


y1 = -6/64 * x^2 + 96/64 * x 


y2 = -8/144 * x^2 + 384 / 144 * x - 3456 / 144


if you graph those equations, you will get:


<img src = "http://theo.x10hosting.com/2014/122101.jpg" alt="$$$" </>


the first equation is modeled by knowing that the zeroes of that eqution are at x = 0 and x = 16.


this means the factors of that equation are (x-0) * (x-16) = 0 which becomes x^2 - 16x = 0


the general equation becomes y = a * (x^2 - 16x)


you know that y = 6 when x = 8, so replace x in that equation to get a * (8^2 - 16(8)) = 6 which becomes a * (-64) = 6 which becomes -64*a = 6 which becomes a = -6/64.


your equation of y = a * (x^2 - 16x) becomes y = -6/64 * (x^2 - 16x) which becomes y = -6/64 * x^2 + 96/64 * x


that's the first equation that was graphed.


the second equation was solved for in a similar manner.


the roots were 12 and 36
the factors were (x-12) * (x-36) = 0
multiplying those factors out got x^2 - 48x + 432 = 0
the general equation became y = a * (x^2 - 48x + 432)
when x was 24, y was 8, so we got 8 = a * (24^2 - 48*24 + 432) which became 8 = 576 * a - 1152 * a + 432 * a which became 8 = -144 * a
divide both sides of that equation by -144 and you get a = -8/144.
your equation becomes y = -8/144 * x^2 + 384/144 * x - 3456/144
that's the equation you see in the graph.