Challenge Project 1/2

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Given the function f(x) = a(x-h)2 k,
Change the values of a, h, and k one at a time.
Step 1: Change the a to 2. What effect does changing the value of a have on the graph when compared to f(x) = x2? Describe in your own words.
Step 2: Change the a to 1/2. What effect does changing the value of a have on the graph when compared to f(x) = x2? Describe in your own words.
Step 3: Change the h to 4. What effect does changing the value of h have on the graph when compared to f(x) = x2? Describe in your own words.
Step 4: Change the h to -4. What effect does changing the value of h have on the graph when compared to f(x) = x2? Describe in your own words.
Step 5: Change the k to 5. What effect does changing the value of k have on the graph when compared to f(x) = x2? Describe in your own words.
Step 6: Change the k to -5. What effect does changing the value of k have on the graph when compared to f(x) = x2? Describe in your own words.
Step 7: Change the a to -2. What effect does changing the value to -a have on the graph when compared to f(x) = x2? Describe in your own words.
Step 8: Go to desmos.com. Create a function that incorporates the transformations from steps 1, 3, and 5. Copy and paste/export the graph from desmos.com to your project file to answer #8. Describe the transformations from the parent function y = x2.
Step 9: Go to desmos.com. Create a function that incorporates the transformations from steps 1, 4, 6, and 7. Copy and paste/export the graph from desmos.com to your project file to answer #9. Describe the transformations from the parent function y = x2.
Step 10: Create a NONQUADRATIC function with at least 3 transformations. Use desmos.com to create a graph of the new function with its parent function on the same grid; and export the graph. State the parent function. Describe the transformations from the parent function.
Challenge Project Part 2: TRIG GRAPHS AND TRANSFORMATIONS

Use the following link to practice with trig graphs and transformations:
https://www.nctm.org/Classroom-Resources/Illuminat…
Change the values of A, B, C and D one at a time.
Using the sin graph provided in the link:
Step 1: Change the A to 2. What effect does changing the value of A have on the graph?Describe in your own words.
Step 2: Change the A to 1/2. What effect does changing the value of A have on the graph? Describe in your own words.
Step 3: Change the B to 2. What effect does changing the value of B have on the graph? Describe in your own words.
Step 4: Change the B to 1/2. What effect does changing the value of B have on the graph? Describe in your own words.
Step 5: Change the C to 90 degrees. What effect does changing the value of C have on the graph? Describe in your own words.
Step 6: Change the C to 180 degrees. What effect does changing the value of C have on the graph? Describe in your own words.
Step 7: Change the D to 2. What effect does changing the value of D have on the graph? Describe in your own words.
Step 8: Change the D to 1/2. What effect does changing the value of D have on the graph? Describe in your own words.
Step 9: Go to desmos.com. Create a new Cosine (cos) trig function that incorporates at least 2 new transformations. Copy and paste/export the graph from desmos.com to this file to answer #9. Describe the transformations from the parent function y = cos x.
Step 10: Graph and export the following parent trig functions to this file.
Sin x
Cos x
Tan x
Sec x
Csc x
Cot x