# Thread: Need help deciphering a function

1. ## Need help deciphering a function

Let P(x) = x^4+ax^3+bx^2+cx+d. The graph of y = P(x) is symmetric with respect to the y-axis, has a relative maximum at (0,1), and has an absolute minimum at (q, -3).

a) Determine the values of a,b,c, and d

b) Find all possible values of q

Thanks if anybody can help.

2. Originally Posted by alakaboom1
Let P(x) = x^4+ax^3+bx^2+cx+d. The graph of y = P(x) is symmetric with respect to the y-axis, has a relative maximum at (0,1), and has an absolute minimum at (q, -3).

a) Determine the values of a,b,c, and d

b) Find all possible values of q

Thanks if anybody can help.
Symmetrix with respect to the y-axis means that $\displaystyle P(x)=P(-x)$ , which forces $\displaystyle a$ and $\displaystyle c$ to be zero.

So now you have:

$\displaystyle P(x)=x^4+bx^2+d$

So $\displaystyle P'(x)=4x^3+2bx$, and so the extrema are at $\displaystyle x=0$, and $\displaystyle x=\pm \sqrt{-b/2}$ , so from the latter we have $\displaystyle -b/2=9$, or $\displaystyle b=-18$.

Can you finish from there?

CB