Polynomial and rational functions
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Absolute Value of a Quadratic Function
Explore and compare the graphs of y = f(x), y = f(|x|), y = |f(x)|, and y = |f(|x|)|.
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Addition and Subtraction of Polynomials
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate … how the graphs change in response.
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Addition of Polynomials - Activity A
Add polynomials using an area model. Use step-by-step feedback to diagnose any problems in the polynomial models and the polynomial addition.
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Addition of Polynomials - Activity B
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes.
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare … direct variation functions to inverse variation functions.
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Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted … polynomial division to the synthetic division.
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Fourth-Degree Polynomials - Activity A
Compare the equation of a fourth‑degree polynomial to its graph. Vary the coefficients of the equation and investigate how the … graph changes in response.
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Fourth-Degree Polynomials - Activity B
Compare the equation of a fourth‑degree polynomial to its graph. Vary the coefficients of the equation and investigate how the … graph changes in response.
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General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore … how the graph changes in response.
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Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of … the function.
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Quadratic and Absolute Value Functions
Compare the graph of a quadratic or absolute‑value function to its equations. Vary the coefficients of the equation and explore how … the graph changes in response.
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Quadratic Inequalities - Activity A
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how … the boundary curve and shaded region change in response.
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Quadratic Inequalities - Activity B
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how … the boundary curve and shaded region change in response.
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Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the … graph and the equation change in response.
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Quadratics in Polynomial Form - Activity A
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph … changes in response.
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Quadratics in Polynomial Form - Activity B
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph … changes in response.
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Quadratics in Vertex Form - Activity A
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response.
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Quadratics in Vertex Form - Activity B
Explore the graph of a quadratic of the form y = a(x − h)2 + k. Vary the terms of the equation and explore how the graph changes … in response. Calculate the location of the vertex and y‑intercepts.
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Quadratics: Polynomial Form in y
Explore the graph of a quadratic of the form x = ay2 + by + c. Vary the coefficients of the equation and examine how the graph changes … in response. Calculate the location of the vertex and y‑intercepts.
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Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated … and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.
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Reflections of a Quadratic Function
Explore and compare the graphs of y = f(x), y = −f(x), y = f(−x), and y = −f(−x), for a … quadratic function f(x) of the form f(x) = ax2 + bx + c. Vary the terms of f(x) and examine how the graphs change in response.
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in … the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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System of Two Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how … the boundary curve and shaded region change in response.
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Zap It! Game
Try to adjust the quadratic function to "Zap" as many data points as possible.
