Anthony P. answered • 03/13/13

Experienced tutor in earth sciences and basic math to trigonometry

h(x) = 2x^{4} + 3x^{3}

Firstly, the function is the sum of a parabolic function with a cubic function (you know what I mean if you know the parent functions y = x^2, and y = x^3). If not graph on a graphing calculator. If you don't have one and you use google chrome, you can download the app Desmos to do it for you. This function will look like a combination of the two.

The roots of the function (x-intercepts) are found by forcing y to be zero and solving for x.

First, factor the polynomial.

0 = x^{3}(2x + 3)

Set each factor equal to zero and solve.

x^{3} = 0 and 2x + 3 = 0

**x = 0 and x = -3/2**

The y-intercept is where x = 0.

**y = 2(0) ^{4} + 3(0)^{3} = 0 **

Robert J.

The end behavior can be found by negelcting the lower degree term(s).

y ~ 2x

^{4}03/13/13