SOLUTION: 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

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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       Log On


   

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(24713) About Me  (Show Source):
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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.




John

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