Answer:
3rd answer : even degree and negative lead coefficient
Explanation:
when you "move" the curve up or down, what are the max. zeroes (interceptions with the x-axis) you can get ?
4 in this case. and the curve has correspondingly 3 local extreme values (the "humps", where the curve changes direction).
that means the degree (the max. exponent of the variable, typically x) of the polynomial is 4 (= the number of potential zeroes, or the number of local extreme values + 1).
which is an even number.
and then, the direction (up or down) of the curve for large values of the variable (typically x) tells us the sign of the lead coefficient :
if it is going down (like in this case), the lead coefficient must be negative.
if it is going up, the lead coefficient must be positive.
simply, because the lead term has the highest exponent and will therefore drive the magnitude of the polynomial result for large values of the variable. if the coefficient of the lead term is negative, then the overall polynomial value is negative (and "down"). if it is positive, then the overall polynomial value is positive (and "up").