find function of graph problem..

[snakeyesxlaw]

The function p is a fourth-degree polynomial with x-intercepts 1, 2, and 9 and y-intercept -2. If p(x) is positive only on the interval (2, 9), find p(x).


- based on whats given, the polynomial is at 4th degree which means its a parabolic type curve at the ends.. but how can you tell if it opens downward or up?

- how to find out which degree is for which intercepts of x?

for example, this is what i am guessing:

(x+1)^2 (x+2) (x+9) - 2


any suggestions?

 

[Deleted member 4993]

The function p is a fourth-degree polynomial with x-intercepts 1, 2, and 9 and y-intercept -2. If p(x) is positive only on the interval (2, 9), find p(x).


- based on whats given, the polynomial is at 4th degree which means its a parabolic type curve at the ends.. but how can you tell if it opens downward or up?

- how to find out which degree is for which intercepts of x?

for example, this is what i am guessing:

(x+1)^2 (x+2) (x+9) - 2


any suggestions?

How can the function be positive only within the domain (2,9) and have a zero at x = 1.

This can only happen if the x axis is tangent to the function at x = 1.(This you got)

If that is so - how does the function look like - opening up or down. Just draw the zeros and pat attention to the restriction on the sign of y.


Your function should look like:

y = A(x-1)^2 * (x-2) * (x-9)

solve for 'A' - by imposing the intercept condition.

Now share with us your work and thought if you need further help.

 

[snakeyesxlaw]

okay, so it opens downward but how do you setup the function for p(x)

(x+9) (x+2)^2 (-x+1) ?

educated guess..

 

[Deleted member 4993]

okay, so it opens downward but how do you setup the function for p(x)

(x+9) (x+2)^2 (-x+1) ?

educated guess..

You have x-intercept at x = 1, 2 & 9

what is the value of p9x) at x=9 - according to your guessed function? what is p(x) at x = 2? What should it be according to information that those are x-intercepts?

Why does it have "^2" with (x+2)?

What form of function did I suggest?

 

[snakeyesxlaw]

okay,

so based on,

-2 = A(x-1)^2 * (x-2) * (x-9)

i get,

A= -1/9

so,

-1/9(x-1)^2 * (x-2) * (x-9)

?

 

[Deleted member 4993]

Now check if it satisfies all the conditions or not...

If not, figure out where you could have gone wrong...