This task will help you explore transformations of functions. It will allow you to see vertical and horizontal shifts, reflections, and nonrigid transformations (stretching and compressing the function). This task uses the example of a quadratic function.

1) By moving the sliders, compare the parent function f(x)=x^2 to f(x)=(x-4)^2 and f(x)=(x-4)^2+3. According to your observations, what does the value of “c” do to the graph? What does the value of “b” do to the graph?
2) Given the parent function f(x)=x^2, predict the effects of the following on the graph:
h(x)=-f(x)
h(x)=f(-x)
Check your prediction by comparing the parent function to the function when “a” equals -1 (this would be –f(x)).
Change “a” back to equal one, and move “d” so that “d” equals -1 (this would be f(-x)).
What type of reflection is h(x)=-f(x)?
What type of reflection is h(x)=f(-x)?
3) Given the parent function f(x)=x^2, predict what the value of “a” will do to the function. Check your prediction by changing the value of "a".
4) Note that the graph f(x)=–(x^2)+2 is reflected over the x-axis and then shifted upward two units. Does the order of transformations matter? Test this by first changing the value of “a” and then changing the value of “c”. Then try this by first changing the value of “c” and then changing the value of “a”.
5) Predict what the graph f(x)= -(x+5)^2+3 would look like. Check your prediction using the sliders.