Expert: Paul Klarreich - 3/4/2006

Question
1) My name is Kimberley i need the answer asap!
2) The question: answer the following questions about this function:  x^4-4x^2
 a)factor the above equation
 b)name the x-intercepts
 c)graph the function
I'm studying many different subjects, I'm in mathematics 151 at lorain county community college, thank you so much for all your help


Answer
Hi, kim,

You wrote:

Subject:  PLEASE HELP!I need the answer by monday

>> That is not a suitable subject.  It's OK to say it, but don't use it as the subject.

Question:  

1) My name is Kimberley i need the answer asap!

2) The question: answer the following questions about this function:
x^4-4x^2

a)factor the above equation

(It's not an equation.  Be careful with your terminology.)

x^4 - 4x^2 has a common factor of  x^2, so we remove that first:

x^2(x^2 - 4)

The second is a difference of squares, so we factor that:

x^2(x + 2)(x - 2)


b)name the x-intercepts

I think you want to LOCATE the x-intercepts.  For each factor, set it equal to zero and solve.  Then you can name them -- John, Shirley, and Alexander, maybe.

x^2 = 0  gives  x = 0.  
x + 2 = 0  gives  x = -2.
x - 2 = 0  gives  x = 2.

Those are the x-intercepts; the points (0,0), (-2,0), (2,0)


c)graph the function

That's a little bit of work, but you can use these facts:

The function is EVEN, containing only even powers of x.  So it is completely symmetric -- the left side looks the same as the right side; if you folded it along the y-axis, the left and right sides would match.

Looking only at the right side, it should come up and pass through (2,0), then zoom up on the right.  

Going back from (2,0) it should rise smoothly to (0,0).

Then you should draw the left side as the mirror image.  If you like, you can:

(1) reply with your email address and I will send you an image of the graph.  (I can't send it through this website -- facilities are very crude.)  Just send a followup question.  I'll know what to do.

(2) Access my plotting program at this link:

ftp://members.aol.com/pklarreich/plotter/

Happy plotting, but you will have to figure it out, I'm afraid.

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I'm studying many different subjects, I'm in mathematics 151 at lorain county community college, thank you so much for all your help

AHA!  I looked it up and I see you are NOT studying calculus, so that limits what you can do.  It is exactly right for you to tell me the course, so I don't get you confused with stuff you haven't studied yet.