Question 520820: 1.Given the function f(x)=1/4(x-2)^2(x+2)^2
2.Find the x and y intercept
3.Determine whether the graph crosess or touches the x axis at each intercept
4.Graph the function
Thanks in advance! Answer by solver91311(16868) (Show Source):
To determine the -intercept, which is the value of the function when substitute for and do the arithmetic:
To find the -intercepts, find the zeros of the function. Since this is a 4th degree polynomial function, there are 4 zeros. (Fundamental Theorem of Algebra). The easiest way to see all four zeros is to write out the function in its fully factored form:
Clearly the zeros are 2 with a multiplicity of 2 and -2 with a multiplicity of 2, for a total of four zeros counting the multiplicities.
A zero that has a multiplicity of 2 occurs where the graph has the -axis as a tangent.
My calculator said it, I believe it, that settles it