Topic: Quadratic Functions
Name ________________________ Date________ Period_______
Worksheet – Writing Polynomial Functions
1. I am a cubic with roots at -2, -3, and 1. (2, 40) is a point on me. Write my function in factored form and sketch me.
2. I’m a cubic with a point at (1, 8) and roots at 2, -1, and 0. Write my function in polynomial form and sketch me.
3. I’m a cubic with a double root at -4 and a root at 2. The point (0, 96) is on me. Write my function in polynomial form and sketch me.
4. I’m a cubic with a double root at 0 and a root at -2 that goes through (3, 90). Write my function in polynomial form and sketch me.
5. I’m a quartic with a triple root at -3 and a root at 2. (-2, 4) is a point on me. Write my function in factored form and sketch me.
6. I’m a quartic with a double root at -1 and a double root at 2. (1,5) is a point on me. Write my function in factored form and sketch me.
7. f(x) has a minimum of -4 at x = 2. Write in polynomial form.
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8. Goes through (1, -36). Write in factored form.
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9. Goes through (2, -108). Write in factored form.
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10. f(x) is a polynomial function that is increasing when x < -1, increasing when x > 3,
decreasing when -1 < x < 3. Write a function with these characteristics and sketch
the graph.
What do you know about the function at x = -1 and x = 3? Justify your answer.
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A 13-3
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[pic]
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A 13-3
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[pic]
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A 13-3
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