Find a formula for the fourth degree polynomial p(x) whose graph is symmetric about the y-axis, and which has a y-intercept of 1, and global maxima at (4,257) and (−4,257).
p(x)=

Question

Find a formula for the fourth degree polynomial p(x) whose graph is symmetric about the y-axis, and which has a y-intercept of 1, and global maxima at (4,257) and (−4,257).
p(x)=

mathmale · Answer

"symmetric about the y-axis" is a sure giveaway:  this function is entirely EVEN (not ODD).

If "global maxima at (4,257)," then your global max on the opposite side of the y-axis is (-4,257).  Great.  You might want to sketch this situation.

Fourth degree poly, entirely even?  Write out the general form:

y = ax^4 + bx^3 + cx^2 + dx + e.

y-intercept is 1?  Then which variable, a, b, c, d or e, would be equal to 1?

Which of the coefficients, a, b, c, d, e, would be zero, and why?

mathmale · Answer

What is the derivative of this function?  Finding it and setting it = to 0 will help you determine more of the coefficients.