Graphing Polynomial Functions: Finding x-Intercepts

[Buddah]

Graph each function given below on a graphing calculator to find a general rule for determining when a graph crosses the x-axis at an x intercept or when the graph just touches and turns away from the x axis. State the rule that you find.

y = (x + 1)^2(x - 2)

y = (x - 4)^3(x - 1)^2

y = (x - 3)^2(x + 4)^4

 

[micromass]

1) This is a homework problem, so it should belong in the homework forums
2) You should post an attempt of the problem
3) What do you expect from us really? That we graph it for you? We can't graph anything on this forum (yet)...

 

[BloodyFrozen]

Agreed with micromass, but here's a hint. Look at the numbers carefully.

 

[Saitama]

For graphing you can use "Microsoft Mathematics". Its really a awesome software.
Give it a try.

 

[Buddah]

okay well i tried to do it

is this correct?

x intercept y=0

y = (x + 1)^2(x - 2)
0 = (x + 1)^2(x - 2)
(x + 1)^2 = 0 =====> x + 1 = 0 =====> x = -1 (-1 , 0)
x - 2 = 0 =====> x = 2 (2 , 0)

y = (x - 4)^3(x - 1)^2
0 = (x - 4)^3(x - 1)^2
(x - 4)^3 = 0 ====> x - 4 = 0 =====> x = 4 (4 , 0)
(x - 1)^2 = 0 ====> x - 1 = 0 ====> x = 1 (1 , 0)

y = (x - 3)^2(x + 4)^4
0 = (x - 3)^2(x + 4)^4
(x - 3)^2 = 0 ====> x - 3 = 0 ====> x = 3 (3 , 0)
(x + 4)^4 = 0 ===> x + 4 = 0 ====> x = -4 (-4 , 0)

 

[Buddah]

Am having trouble explaining it

 

[BloodyFrozen]

From what I understand of your original post, you do not need to do all that work. It's simple, look at the graphs.

Hint: Take notice of the powers (not just by degree) to determine whether it goes right through or only touches.

EDIT: By the way, recall what multiplicity is.


The last function might be a little hard to view, but that should not affect your rule.

It might help to recognize how x² and x³ look like.

 

[Hells]

Yes it's correct, now try plugging in some numbers that make the factors negative :)