Grade 11 · Polynomial roots
Polynomial roots · Investigation 1 of 100
Polynomial roots: Opposite roots centered at zero
Polynomial roots: investigate opposite roots centered at zero with first root a = -2; second root b = 2.
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100 guided animations · 10 topic units · Free to explore
Grade 11 mathematics,
one moving idea at a time.
Make a prediction, change a value, and explain the result. Work through each unit in order or choose the topic you want to understand today. Every investigation has controls, a worked explanation, and a question to test your reasoning.
Your collection at a glance
Ten topics. Ten investigations in each.
- UNIT 1
Polynomial roots
Investigations 1–10
- UNIT 2
Rational functions
Investigations 11–20
- UNIT 3
Logarithms and domains
Investigations 21–30
- UNIT 4
Exponential calibration
Investigations 31–40
- UNIT 5
Geometric sums
Investigations 41–50
- UNIT 6
Complex polar form
Investigations 51–60
- UNIT 7
Trigonometric periods
Investigations 61–70
- UNIT 8
Triangle area and angle
Investigations 71–80
- UNIT 9
Quadratic sequences
Investigations 81–90
- UNIT 10
Rescaling data
Investigations 91–100
Related investigations use the same mathematical model with different questions and starting values. Reset restores the values used in that investigation’s worked answer. Read its assumptions before applying a model to a new situation.
Explore the Grade 11 collection.
100 animations · Showing 1–20
Grade 11 · Polynomial roots
Polynomial roots · Investigation 2 of 100
Polynomial roots: A repeated positive root
Polynomial roots: investigate a repeated positive root with first root a = 1; second root b = 1.
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Polynomial roots · Investigation 3 of 100
Polynomial roots: A repeated negative root
Polynomial roots: investigate a repeated negative root with first root a = -2; second root b = -2.
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Polynomial roots · Investigation 4 of 100
Polynomial roots: One intercept at the origin
Polynomial roots: investigate one intercept at the origin with first root a = 0; second root b = 3.
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Polynomial roots · Investigation 5 of 100
Polynomial roots: Two positive intercepts
Polynomial roots: investigate two positive intercepts with first root a = 1; second root b = 3.
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Polynomial roots · Investigation 6 of 100
Polynomial roots: Two negative intercepts
Polynomial roots: investigate two negative intercepts with first root a = -3; second root b = -1.
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Polynomial roots · Investigation 7 of 100
Polynomial roots: An asymmetric pair across zero
Polynomial roots: investigate an asymmetric pair across zero with first root a = -1; second root b = 3.
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Polynomial roots · Investigation 8 of 100
Polynomial roots: A narrow interval of negative values
Polynomial roots: investigate a narrow interval of negative values with first root a = 1; second root b = 1.5.
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Polynomial roots · Investigation 9 of 100
Polynomial roots: A wide six-unit root gap
Polynomial roots: investigate a wide six-unit root gap with first root a = -3; second root b = 3.
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Polynomial roots · Investigation 10 of 100
Polynomial roots: Half-unit roots and symmetry
Polynomial roots: investigate half-unit roots and symmetry with first root a = -0.5; second root b = 1.5.
Explore animationGrade 11 · Rational functions
Rational functions · Investigation 11 of 100
Rational functions: A reciprocal centered at zero
Rational functions: investigate a reciprocal centered at zero with numerator a = 1; pole location b = 0.
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Rational functions · Investigation 12 of 100
Rational functions: Move the pole two units right
Rational functions: investigate move the pole two units right with numerator a = 1; pole location b = 2.
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Rational functions · Investigation 13 of 100
Rational functions: Move the pole two units left
Rational functions: investigate move the pole two units left with numerator a = 1; pole location b = -2.
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Rational functions · Investigation 14 of 100
Rational functions: Double the right branch
Rational functions: investigate double the right branch with numerator a = 2; pole location b = 0.
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Rational functions · Investigation 15 of 100
Rational functions: Halve the numerator
Rational functions: investigate halve the numerator with numerator a = 0.5; pole location b = 0.
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Rational functions · Investigation 16 of 100
Rational functions: Tall branch with a positive pole
Rational functions: investigate tall branch with a positive pole with numerator a = 4; pole location b = 1.
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Rational functions · Investigation 17 of 100
Rational functions: Negative pole and triple scale
Rational functions: investigate negative pole and triple scale with numerator a = 3; pole location b = -1.
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Rational functions · Investigation 18 of 100
Rational functions: A half-unit domain shift
Rational functions: investigate a half-unit domain shift with numerator a = 1.5; pole location b = 0.5.
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Rational functions · Investigation 19 of 100
Rational functions: A near-zero pole on the left
Rational functions: investigate a near-zero pole on the left with numerator a = 2.5; pole location b = -0.5.
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Rational functions · Investigation 20 of 100
Rational functions: Combine translation and large scale
Rational functions: investigate combine translation and large scale with numerator a = 3.5; pole location b = 1.5.
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