Question

Sketch the following:
A) Quadratic polynomial with exactly 1 zero
B) Cubic polynomial with exactly 3 zeros
C) Quartic polynomial with exactly 3 zeros
D) Quintic polynomial with exactly 4 zeros
E) Quartic polynomial with no zeros
F) Quintic polynomial with exactly 5 zeros

Answer 1

each graph should require 1 less than the degree number of points in order to graph

Answer 2

at most that many i believe

Answer 3

so each degree polynomial can change direction from increasing to decreasing at most the degree -1 times, right?

Answer 4

like a 4th degree one can make a W shape... turns around in y direction 3 times at most

Answer 5

i think the number of zeros can depend on how much you shift the graph up or down

Answer 6

Just draw the general shape with the most times of increasing to decreasing changes, and move it up or down till you get the number of x-intercepts you want

Answer 7

What would C look?