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.
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 y-axis. Compare the two graphs and explain the reflection of the graph of f(x) in the y-axis.
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 y-axis. 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 x-axis.
Reflection Of Graphs Of Functions.