Posted by **Destiny** on Tuesday, October 21, 2008 at 11:08pm.

HELP!!!!!!!!!!!!!

write equation of a polynomial function with the given characteristics.

Leading coefficient is 1 or -1

crosses the x axis at -2,3, and 4

touches the x axis at 0

lies above the x axis between -2 and 0

- algebra -
**Reiny**, Tuesday, October 21, 2008 at 11:26pm
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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