12 grade student-george
Let P(x) = x4 + ax3 + bx2 + cx + d. The graph of y = P(x) is symmetric with respect to the y-axis, has a relative max. at (0,1) and has an absolute min. at (q, -3)
a) determine the values for a, b c, and d using these values, write an equation for P(x)
Since P(x) is symmetric in the y-axis, P(x) = P(-x) for any number x. Thus
The graph of y = P(x) passes through (0,1) and hence P(0) = 1. This will tell you the value of d.
Finally (q,-3) is on the curve so P(q) = -3 and using what you know about absolute minima should give you a second equation that will allow you to solve for q.I hope this helps,