Turning points

What this lesson shows

A polynomial of degree 4. How many times can its graph change direction — go from climbing to falling, or falling to climbing?

Try it yourself

Real questions from this lesson's worksheets — answers below each one.

1. A polynomial of degree 2 has at most how many turning points?
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   1
2. f(x) = 2x² - 3x + 1 has at most how many turning points?
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   1
3. For f(x) = (x − 2)³(x + 1), at x = 2 the graph ___ the x-axis.
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   crosses
4. True or false: every polynomial of degree 2 has exactly 1 turning point.
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   True