GistBook Algebra 2

ginny gist, Apr 27, 2014

Table of Contents

  1. Conic Sections
    1. Basketball take 2
    2. Hoover Dam Bypass Bridge
    3. Dancing Fountains Parabola
    4. Floating Midpoints and Ellipses
    5. Section 10.5-Reflection Property of Ellipse
    6. Hyperbola--Matching curve to nuclear cooling towers.
    7. Elliptical Billiard Table
    8. Section 10.5-Hyperbola Reflection
    9. the reflective property of hyperbola
    10. the reflective property of ellipse
    11. ellipse construction
    12. Hyperbolas
  2. Exponential and Logarithmic Functions
    1. Investigating Exponential Growth and Decay: f(x) = a(b^x)

1.

Conic Sections

  • 1. Basketball take 2
  • 2. Hoover Dam Bypass Bridge
  • 3. Dancing Fountains Parabola
  • 4. Floating Midpoints and Ellipses
  • 5. Section 10.5-Reflection Property of Ellipse
  • 6. Hyperbola--Matching curve to nuclear cooling towers.
  • 7. Elliptical Billiard Table
  • 8. Section 10.5-Hyperbola Reflection
  • 9. the reflective property of hyperbola
  • 10. the reflective property of ellipse
  • 11. ellipse construction
  • 12. Hyperbolas

1.1.

Basketball take 2

Use the sliders to match the parabola to the arch of the ball.
– higginsva

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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2.

Exponential and Logarithmic Functions

  • 1. Investigating Exponential Growth and Decay: f(x) = a(b^x)

2.1.

Investigating Exponential Growth and Decay: f(x) = a(b^x)

This application will help us explore exponential functions. We will look at functions of the form f(x) = a(b^x), where a is a positive real number and b > 0 but b is not 1. This applet will help you understand how changing the values of a and b affect the shape of the graph.
Investigating Exponential Growth and Decay: f(x) = a(b^x)
Questions:[br]1. Pick a value for a. Then, slide the value for b. For five different values for b, write the function's equation and sketch a graph of the function with the y-intercept labeled. For example, if I pick a = 2 and b = 3, then the equation is f(x) = 2(3^x). Don't be afraid to use decimals!![br]2. Describe how changing the value of b changes the graph of the function.[br]3. Of your five selected functions, which graphs represented growth and which represented decay? Explain how you can determine if a function is exponential growth or decay based on the equation of the function, not the graph.[br]4. Pick a value for b. Then, slide the value for a. For three different values of a, write the function's equation and sketch a graph of the function with the y-intercept labeled. See the example in 1.[br]5. Explain how the value of a changes the graph of the function.[br]6. Based on your observations, how do a and b affect whether or not the graph is exponential growth or exponential decay?[br]7. Based on your observations, how do a and b affect the rate of increase or decrease in an exponential function?
– Mr. Bokar

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