# Determine an equation for

• September 14th 2013, 08:04 AM
tdotodot
Determine an equation for
Determine an equation for the graph of the polynomial function shown...

There's a graph that goes from x-axis: -2 to +2 and y-axis:+4 to -4.
There are three zero's marked at: -1, 0, +2
There is one point given at: (-1,-2)
The graph starts from the bottom goes up towards -1(x-axis) then curves and goes through zero, down to the point (-1,-2), curves at that point and goes up through the point (2,0). The curves are consistent in size.

So what I was thinking was something like:

y = a (x+1)(x-2)^2
or
y = 1 (x+1)(x-2)^2
...This get's me somewhat close but is not correct.
I know you need +1 and -2 in brackets, since these will be opposite of the zero's which are -1 and +2.

__________________________________________________ _________________

Sort of related so I though I'd ask in the same thread. This is a different question.
Determine an equation in factored form for the polynomial function with zeros 2 (order2), 2/3, and 3 that passes through the point (1,6).

What does "(Order 2)" mean? What are orders? I know zero's are where the graph hit's 0-on-the-x-axis. How would I start this question?
• September 14th 2013, 09:04 AM
HallsofIvy
Re: Determine an equation for
Quote:

Originally Posted by tdotodot
Determine an equation for the graph of the polynomial function shown...

There's a graph that goes from x-axis: -2 to +2 and y-axis:+4 to -4.

I assume this only means that the area in which the graph is shown is -2< x< 2, -4< y< 4, not that the graph includes the points (-2, 4) and (2, -4)

[quote]There are three zero's marked at: -1, 0, +2
So we have (-1, 0), (0, 0), and (2, 0) which means, assuming this is a polynomial, we have factors of x+ 1, x, and x- 2.

Quote:

There is one point given at: (-1,-2)
That's contradictory- you said above that was a 0 at -1 and if the graph of a function goes through (-1, 0) it cannot also go through (-1, -2).

Quote:

The graph starts from the bottom goes up towards -1(x-axis) then curves and goes through zero, down to the point (-1,-2), curves at that point and goes up through the point (2,0). The curves are consistent in size.

So what I was thinking was something like:

y = a (x+1)(x-2)^2
or
y = 1 (x+1)(x-2)^2
...This get's me somewhat close but is not correct.
I know you need +1 and -2 in brackets, since these will be opposite of the zero's which are -1 and +2.
This is impossible. If this is the graph of any function, it [b]cannot go through both (-1, 0) and (-1, -2).

Quote:

__________________________________________________ _________________

Sort of related so I though I'd ask in the same thread. This is a different question.
Determine an equation in factored form for the polynomial function with zeros 2 (order2), 2/3, and 3 that passes through the point (1,6).

What does "(Order 2)" mean? What are orders? I know zero's are where the graph hit's 0-on-the-x-axis. How would I start this question?
I suspect that "order of a zero" is defined in the text where you got this problem. A zero, a, of a polynomial is of "order n" if the polynomial has a factor of $(x- a)^n$.
Saying that this polynomial function has "zeros 2 (order2), 2/3, and 3" means it is (at least) of the form [ex]y= a(x- 2)^2(x- 2/3)(x- 3)[tex]. Assuming there are no other factors you can determine a so that the graph "passes through the point (1,6)" by setting x= 1, y= 6 in that and solving for a.
• September 14th 2013, 09:40 AM
tdotodot
Re: Determine an equation for
[QUOTE=HallsofIvy;796996]I assume this only means that the area in which the graph is shown is -2< x< 2, -4< y< 4, not that the graph includes the points (-2, 4) and (2, -4)

Quote:

There are three zero's marked at: -1, 0, +2
So we have (-1, 0), (0, 0), and (2, 0) which means, assuming this is a polynomial, we have factors of x+ 1, x, and x- 2.

That's contradictory- you said above that was a 0 at -1 and if the graph of a function goes through (-1, 0) it cannot also go through (-1, -2).

This is impossible. If this is the graph of any function, it [b]cannot go through both (-1, 0) and (-1, -2).

I suspect that "order of a zero" is defined in the text where you got this problem. A zero, a, of a polynomial is of "order n" if the polynomial has a factor of $(x- a)^n$.
Saying that this polynomial function has "zeros 2 (order2), 2/3, and 3" means it is (at least) of the form [ex]y= a(x- 2)^2(x- 2/3)(x- 3)[tex]. Assuming there are no other factors you can determine a so that the graph "passes through the point (1,6)" by setting x= 1, y= 6 in that and solving for a.
I might not have explain the graph (first question) in the best way. I took a pic and uploaded it so you can see the graph. The close up won't upload but that should be fine.
Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting

____________________

Second question, so pretty much what they mean by order is the exponent to the term? So zeros -3 (order3) and zero +535 (order34) would be -3^3 and 535^34 respectively?
• September 14th 2013, 10:47 AM
HallsofIvy
Re: Determine an equation for
Quote:

Originally Posted by tdotodot
Determine an equation for the graph of the polynomial function shown...

There's a graph that goes from x-axis: -2 to +2 and y-axis:+4 to -4.
There are three zero's marked at: -1, 0, +2
There is one point given at: (-1,-2)

On the graph you now show that is (1, -2), not (-1, -2)!
So this must be of the form y= a(x+ 1)x(x- 2). To find a, set x=1, y= -2 in that and solve for a.

Quote:

The graph starts from the bottom goes up towards -1(x-axis) then curves and goes through zero, down to the point (-1,-2), curves at that point and goes up through the point (2,0). The curves are consistent in size.

So what I was thinking was something like:

y = a (x+1)(x-2)^2
or
y = 1 (x+1)(x-2)^2
...This get's me somewhat close but is not correct.
I know you need +1 and -2 in brackets, since these will be opposite of the zero's which are -1 and +2.

__________________________________________________ _________________

Sort of related so I though I'd ask in the same thread. This is a different question.
Determine an equation in factored form for the polynomial function with zeros 2 (order2), 2/3, and 3 that passes through the point (1,6).

What does "(Order 2)" mean? What are orders? I know zero's are where the graph hit's 0-on-the-x-axis. How would I start this question?
• September 14th 2013, 10:51 AM
HallsofIvy
Re: Determine an equation for
Quote:

Originally Posted by tdotodot
Second question, so pretty much what they mean by order is the exponent to the term? So zeros -3 (order3) and zero +535 (order34) would be -3^3 and 535^34 respectively?

No, that's not what I said. We are talking about polynomial functions not just numbers. If you are told that a polynomial function has a "zero of order 3 at -3 and a zero of order 34 at 535" then the polynomial has factors $(x+3)^3(x- 535)^{34}$, possibly with other factors.