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Easy: Zeros
The zeros are where the graph meets the x-axis. If it crosses, the zero has odd multiplicity; if it only touches and turns back, the factor is squared. The end behavior depends on the degree and the sign of the leading coefficient: even degree means both ends go the same way, odd degree means they go opposite ways, and a negative leading coefficient flips the picture. To find the leading coefficient a, substitute the y-intercept into y = a(x − r₁)(x − r₂)….
Use the graph of each polynomial function to answer the question.
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At most one fewer than its degree. A cubic has at most 2 turns and a quartic at most 3.
At a zero of odd multiplicity the graph crosses the x-axis; at a zero of even multiplicity it touches the axis and turns back. A triple zero crosses with a flattened S shape.
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