Answer:
D
Explanation:
a quartic function is a polynomial of the 4th degree. that means that in the function expression the highest exponent of a term of x is 4.
y = ax⁴ + bx³ + cx² + dx + e
with a not 0.
the degree of a polynomial expression defines also how many zeroes (x values that create y = 0, that means points where the graph intersects the x-axis) there are.
a function has as many zeroes as the degree of the polynomial.
so, we are looking for potentially 4 zeroes.
the only graph that fulfills that is D.
the left "touch" of the graph on the x-axis counts for 2 (but equal) zeroes.
you can always test by virtually shifting the graph up or down and see, what are the max. x-axis intersections you can create.
if shifting D down a little bit you see, that this left "touch" turns into 2 intersections.
the same would apply for a "bend" or turn in the graph that does not even touch the x-axis.
if the original graph has not enough real x-axis intersections, it means that the remaining zeroes are then "imaginary" complex numbers (based on the sqrt(-1) = i).
a polynomial of the nth degree, must have n zeroes.
as a consequence it must have n-1 turns (even if the corresponding curve segments don't intersect with the x-axis in the real number space).