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Playing with Functions

Composition of Functions (Algebra II)+ 
Java Applet 
Tool 

[1]

Students choose one or two functions and perform a variety of operations (adjusting parameters; combining through addition, multiplication, or composition; reflecting; others possible).
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Polynomial Function Graphs

Polynomials (Algebra II) 
Java Applet 
Tool 

[0]

Students can look at graphs of degrees 0 through 5 and see the effects of changing the coefficients a, b, c, d and e on each graph by moving sliders. Allows students to see how the different cubic fu...
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Polynomial Roots Applet

Polynomials (Algebra II) 
Java Applet 
Tool 

[2]

This applet solves only the real roots of polynomial equations up to a maximum of order five. Complex number solutions are not available, however it can be included in the future if users request s...
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Polynomials and Their Order

Polynomials (Algebra II) 
Java Applet 
Tool 

[0]

Students are given 7 polynomials and asked to determine their degree (order) and drag and drop the description so that it matches the polynomial. Immediate feedback is given.
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Problem of Hyperbola

Hyperbolas (Algebra II) 
Java Applet 
Tool 

[0]

The defintion of a hyperbola is illustrated using this applet. When concentric circles are formed at each of the foci, the intersections of the circles must satisfy the constant difference.
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Proof Without Words: Completin...

Completing the square (Algebra II) 
Java Applet 
Tool 

[2]

Carry out an interactive, geometric "proof without words" for the algebraic technique of completing the square.
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Quadratic Equations 2

Completing the square (Algebra II)+ 
Java Applet 
Tool 

[1]

Choose values of p and q in the equation x^2 + px + q = 0, and see determinations of the real roots by completing the square and use of the quadratic formula as well as a graphical visualization of th...
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Quadratic Function Applet

Vertex form (Algebra II)+ 
Java Applet 
Tool 

[0]

Students graph a quadratic function in vertex form by using a, h and k sliders. The applet makes the translations, reflections and stretches very visual and clear. There are no exercises or supportin...
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Quadratic Relations: Parabola ...

Parabolas (Algebra II) 
Java Applet 
Tool 

[0]

This applet allows the user to explore the graphs of horizontal of vertical parabolas in vertex form by using sliders to adjust a, h and k. The equation changes with the change in a, h and k on the s...
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Quadratic equation visualizer

Standard form (Algebra II)+ 
Java Applet 
Tool 

[1]

Explore how the parameters in a quadratic equaiton in standard form affect the graph of the equation. Dynamically change the parameters a, b, and c and immediately see the effect on the graph. Try t...
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Radical Practice

Simplify Expressions (Algebra II) 
Java Applet 
Tool 

[1]

Practice simplifying simple square roots, square roots with numbers outside the radical, simple cube roots, and cube roots with numbers outside the root. There is no practice with variables under the...
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Rational Equations Visualizer

Horizontal shift (Algebra II)+ 
Java Applet 
Tool 

[2]

Explore how the parameters in a rational equation affect the graph of the equation. Dynamically change the parameters and immediately see how the graph changes. Undefined points are clearly visible....
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Recognize Functions 1

Graphing (Algebra II)+ 
Java Applet 
Tool 

[1]

Use your knowledge of linear and quadratic functions to match each graph with its function.
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Recognize Graphs 1

Graphing (Algebra II)+ 
Java Applet 
Tool 

[1]

Use your knowledge of quadratic functions to match each function with its graph. Functions are of the form ax^2 + bx + c.
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Recognize Graphs 2

Transformations of functions (Algebra II)+ 
Java Applet 
Tool 

[1]

Use your knowledge of rational functions to match the equation with its corresponding graph. Equations are of the form a + b/x or a + b/x^2.
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Recursion

Recursion and special sequences (Algebra II) 
Java Applet 
Tool 

[0]

This activity graphs recursive functions of the form f(0) = C, defining f(n) based on f(n  1).
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Reflective Properties of Ellip...

Ellipses (Algebra II) 
Java Applet 
Tool 

[0]

Interactive page to demonstrate the reflective properties of ellipses.
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Reflective Properties of Hyper...

Hyperbolas (Algebra II) 
Java Applet 
Tool 

[0]

Interactive page to demonstrate the reflective properties of hyperbolas.
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Savings Calculator

Growth and decay applications (Algebra II)+ 
Java Applet 
Tool 

[0]

Explore how savings, with or without regular deposits, grow over time.
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Savings Calculator

Growth and decay applications (Algebra II) 
Java Applet 
Tool 

[0]

Use this savings calculator to see how a consistent approach to investing can make your money grow. Whether saving for a house, a car, or other special purchase, the savings calculator will help you d...
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Scaling

Transformations of functions (Algebra II) 
Java Applet 
Tool 

[0]

Students explore transformations to linearize data.
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Sequence Puzzle

Arithmetic sequences and series (Algebra II)+ 
Java Applet 
Tool 

[0]

Students are given 8 sequences and must determine if they are geometric or arithmetic. As they answer correctly, a photographic puzzle of the Little Rascals is assembled.
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Shedding Light on the Subject

Growth and decay applications (Algebra II) 
Java Applet 
Tool 

[0]

This is a full lesson that gives students experience with exponential functions in an application format. There is a movie, an applet for gathering information, and a graphing applet. There is a les...
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Smithmath Customizable Graphin...

Parent Functions (Algebra II)+ 
Java Applet 
Tool 

[0]

Play this customizable game by entering functions that "hit" certain coordinates while avoiding others. Players (or teachers) can add as many of the coordinates to target or avoid, as well as set colo...
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Squares and Similar Things

Binomial Expansion (Algebra II) 
Java Applet 
Tool 

[1]

Use your knowledge of binomial expansion and the FOIL method to match each expression with its corresponding expanded and simplified expression.
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