Need help with deciphering a function

[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 minimum at (0,1), and has an absolute minimun at (q, -3).

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

b) Find all possible values of q

I think c =0, and d =1......but im really not sure. I really couldn't get too far into the problem, so I need help with the whole thing.

Thanks if anybody can help.

 

[wjm11]

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 minimum at (0,1), and has an absolute minimun at (q, -3).

Is there possibly a typo in the problem statement? Is it possible we have a "relative maximum" at (0,1)?

 

[fasteddie65]

As far as symmetry, if the graph is symmetric to the y-axis, try setting f(x) = f(-x) and see what you can find out from that.

 

[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 minimum at (0,1), and has an absolute minimun at (q, -3).

Is there possibly a typo in the problem statement? Is it possible we have a "relative maximum" at (0,1)?

Yes....... . Sorry about that, i just typed it wrong, ill fix it now. it should be relative maximum and and absolute minimum.

 

[wjm11]

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

I think c =0, and d =1......but im really not sure.

FastEddie said:

try setting f(x) = f(-x) and see what you can find out from that.

You are correct that d = 1. This can be determined by plugging in 0 for x and 1 for y, knowing that the point (0,1) is a solution.

How did you determine that c = 0? (I just want to follow your logic.) Follow FastEddie’s advice. (From that you should discover that both a and c are equal to 0.)