• If the polynomial is odd (it has an odd power) then its end are going to go in opposite directions (like a linear equation which has an odd power)
• If a polynomial is even (it has an even power) then both its ends will go in the same direction. If the lead coefficient is positive the ends will finish up, if it is odd then they will finish down (like a quadratic).
• If a polynomial is odd and its lead coefficient is postive, then it will head up on the right hand side and down on the left hand side (like a linear equation).
• If a polynomial is odd and its lead coefficient is negative, then it will head down on the right hand side and up on the left hand side (like a linear equation).
• The maximum number of x-intercepts equals the degree of the polynomial. The maximum number of turning points is one less than the degree of the polynomial. So, if the degree is n, the maximum number of turning points is n - 1.
  For example : if y = 3x⁵ + 4x⁴ - 3x³ + 2x + 4
  there are 4 turning points and there are 5 roots (some may be imaginary - not hitting x line)