Reflection Of Graphs In y-axis

This is an applet to explore the reflection of graphs in the y-axis by comparing the graphs of f(x)(in blue) and h(x) = f(-x) (in red).

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.

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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 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.

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