Functions

**uniquereason81** · April 22nd 2008, 06:17 AM

Hey guys, I have a big test coming up and I need to know how to do these problems. So thanks if you can help or even taking the time to look at them.

Given the function f(x) = x^(3) - 3x^(2) + 2x

(A) find the real roots (x-intercepts)

(B) what is the y-intercept

**red_dog** · April 22nd 2008, 06:20 AM

To find the x-intercept you must solve the equation $f(x)=0$ .
Then $x^3-3x^2+2x=0\Leftrightarrow x(x-1)(x-2)=0$

To find the y-intercept you have to calculate $f(0)$

**uniquereason81** · April 22nd 2008, 06:23 AM

sorry im still confuse

**red_dog** · April 22nd 2008, 06:27 AM

$x(x-1)(x-2)=0\Rightarrow x_1=0, \ x_2=1, \ x_3=2$
So, the x-intercepts are $O(0,0), \ A(1,0), \ B(2,0)$

$f(0)=0$ , so the y-intercept is $O(0,0)$

**mr fantastic** · April 22nd 2008, 06:31 AM

Originally Posted by uniquereason81

sorry im still confuse

What are you confused about??
Do you understand how the factorised form $x(x-1)(x-2)$ of f(x) is got?
Do you know how to solve the equation $x(x-1)(x-2)=0$ ?
Do you know what calculate f(0) means? Do you know why you have to calculate it?

There's not a lot to get confused over ...... How much work have you actually done in preparing for the big test?

**uniquereason81** · April 22nd 2008, 06:32 AM

so you unfoil the eaquation , set it to zero

**uniquereason81** · April 22nd 2008, 06:33 AM

i just don't want to over look anything

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