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Math 2

PatriciaJensen, Dec 12, 2016

1. Transformations of Graphs (a, h, k)
2. Reflection in y-axis
3. Central and Inscribed Angles
4. Angles Created by Two Parallel Lines Cut by a Transversal
5. Transversal Intersects Parallel Lines
6. Explore the Basic Trig Functions of a Right Triangle
7. SOH-CAH-TOA's Failure (II)
8. Angles Formed By Intersecting Chords
9. Circle Equation: Center NOT (0,0)
10. Triangle Angle Sum Theorem
11. Exterior Angle Theorem
12. Triangle Sides and Angles
13. Lengths of Segments formed by Intersecting Chords
14. Euclid's Elements - Book III, Proposition 14
15. Intersecting Chords Angle Measure Theorem
16. Equation of a Circle
17. Copy of Multiplying Polynomials using Algebra Tiles
18. Completing the Square (2)

Information

1.

Transformations of Graphs (a, h, k)

Consider the function y = f(x). We're going to refer to this function as the PARENT FUNCTION. The following applet allows you to select one of 4 parent functions: The basic quadratic function: f(x) = x^2 The basic cubic function: f(x) = x^3 The basic absolute value function: f(x) = |x| The basic square root function: y = sqrt(x) In each of these functions, you will investigate what the parameters "a", "h", & "k" will do the graph the parent function y = f(x) when we graph the function y = a*f(x - h) + k The following applet allows you to use a slider to change the values of different parameters of 4 key functions. The parameters are "a", "h", and "k". Within the following applet, change the slider values for "a", "h", and "k". As you do, pay attention to how the equation of the graph changes as you use the slider to change a certain parameter. Be sure to pay close attention as you change parameters, one at a time, for EACH of the four functions listed below. After interacting with this applet for a few minutes, answer the questions (below the applet) as specifically as you can.

Questions: 1) For any value "h", how does the parameter "h" affect the graph of a function? If h > 0, what happens? If h < 0, what happens? 2) For any value "k", how does the parameter "k" affect the graph of a function? If k > 0, what happens? If k < 0, what happens? 3) For any value "a", how does the parameter "a" affect the graph of a function? If a > 0, what happens? If a < 0, what happens?