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

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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

Mathematics
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each graph should require 1 less than the degree number of points in order to graph
at most that many i believe
so each degree polynomial can change direction from increasing to decreasing at most the degree -1 times, right?

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like a 4th degree one can make a W shape... turns around in y direction 3 times at most
i think the number of zeros can depend on how much you shift the graph up or down
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
What would C look?

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