h(x)=2x4th + 3x3rd

Question

need to be able to graph the polynomial functions .  Have to identify x-intercept(s), y-intercept and describe the end behavior of the function

 

 

Answer 1

Be careful of how many times each answer occurs. x=0 three times, so you would write the answer as x=0 mult 3, where mult is short for multiplicity. While the overall graph may look similar to a parabolic, the graph at the zeros will be shaped like the parent functions y=x and y=x³ . The graph at x=-3/2 will resemble a line, and the graph at x=0 will look like a cubic function. By knowing the intercepts, the multiplicity, and the end behavior, you don't need a calculator to graph this function.

Answer 2

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