Question

Hi I would like help solving this exercise:
Consider the function
f (x)= |x^2 -6x+3|
a- graph f
I know what absolute value means, and I found the solution to x^2-6x+3= 0; it's 5 and 1. But I don't understand how to graph it.
I know that |x|= x if x> 0 and -x if x <0. But how can I translate it to the graph. Thanks

Answer 1

You can graph it by putting it in a CAS program. When it is in | |, then it only spits positive values on the y axis.
http://www.wolframalpha.com/input/?i=f(x)%3D%7Cx%5E2-6x%2B3%7C

Answer 2

Thanks for the tip I have a similar software. The thing is I'm studying for precalc finals and I have to understand why the graph turns out that way, because after I graph it there are several questions to be answered. Like: When does the function has 4 different y values ?

Answer 3

If you can graph \(x^{2}-6x+3\) Normally, then you can easily graph the absolute value of it. Are you comfortable with graphing \(x^{2}-6x+3?\)

Answer 4

@tatianagomezb

Answer 5

And if you found solutions to be 5 and 1, then your function should be \(x^{2}-6x+5\) or some multiple of it.

Answer 6

Yes

Answer 7

Did you mean \(x^{2}-6x+5?\)

Answer 8

Hold on

Answer 9

Yes, typo. Yes it is x^2 -6x +5

Answer 10

Okay. So would you be comfortable enough using the draw tool on here to graph \(x^{2}-6x+5?\)

From there I can easily show you how to get the absolute value version.

Answer 11

Okay,

Answer 12

Done

Answer 13

Did the graph get posted? I don't see that you posted the graph, lol.

Answer 14

I'm on my phone, I don't rleally know
Here http://www.cymath.com/answer.php?q=graph%20y%3Dx%5E2-6x%2B5

Answer 15

Oh, I see. That complicates using the draw tool then, lol. Alright, Ill draw it out and show ya.

Answer 16

I wanted to upload the screen shot but I couldn't

Answer 17

Bad graph, but whatever. Still will show the idea.