The function f(x) is a quadratic function of the form
f(x) = ax^{ 2} + bx + c
The exploration is carried out by changing the parameters a, b and c included in f(x) above. Follow the tutorial below.
TUTORIAL
1  click on the button above "click here to start" and MAXIMIZE the window obtained.
2  Use the sliders to set parameter a to zero, parameters b and c to a non zero value; f(x) is a linear function. Compare the graph of f(x) in blue and that of f(x) in red. Explain (Hint: Compare the positions of points (x,f(x)) and (x,h(x)) and note that h(x) = f(x))
3  Select non zero values for a, b and c to obtain quadratic functions with graphs not symmetric with respect to yaxis. Compare the two graphs and explain the reflection of the graph of f(x) in the yaxis.
How can the graph of f(x) be obtained from that of f(x)?
4  Select non zero values for a, and c and set b = 0 to obtain quadratic functions with graphs symmetric with respect to yaxis. Compare the two graphs and explain why the graph of f(x) and h(x) are the same.
More on reflections:
Reflection Of Graphs In xaxis.
Reflection Of Graphs Of Functions.
