Posted by Destiny on Tuesday, October 21, 2008 at 11:08pm.
from "touches the x axis at 0", we can see a double root of x=0 at the origin, meaning the curve must touch the x-axis at the origin without crossing.
But it does cross at x = -2,3 and 4
so we would have
y = ±1(x^2)(x+2)(x-3)(x-4)
[think of the x^2 as (x-0)(x-0)]
make a sketch with intercepts as I have indicated, having the curve rise to infinity in the 1st, and to negative infinity in the 3rd quadrants,
for the curve to be above the x-axis between -2 and 0
so the coefficient has to be +1
so y = (x^2)(x+2)(x-3)(x-4)
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