Reflection Of Graphs on the y-axis

This is an html 5 applet to explore the reflection of graphs on the y-axis by comparing the graphs of f(x) (in blue) and 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.


a =

b =

c =

TUTORIAL 1 - click on the button "draw" to start.

2 - The initial values of a, b and c are 1 , 2 and -1 respectively. Compare the graph of f(x) in blue and that of f(-x) in red. Compare the positions of points (x,f(x)) and (x , f(-x)). Select and experiment with other values of a, b and c.

3 - Select values for a, b and c to obtain quadratic functions with graphs symmetric with respect to y-axis. Compare the two graphs and explain the reflection of the graph of f(x) in the y-axis. Why are the graphs the same? Can you prove it analytically?

4 - How can the graph of f(-x) be obtained from that of f(x)? .

5 - Why do the graph of f(-x) and that of f(x) have a common point at x = 0? .

More on reflections:

Reflection Of Graphs In x-axis.

Reflection Of Graphs Of Functions.