h(x) = 2x4 + 3x3
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 = x3(2x + 3)
Set each factor equal to zero and solve.
x3 = 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