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 "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 yaxis. Compare the two graphs and explain the reflection of the graph of f(x) in the yaxis. 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 xaxis.
Reflection Of Graphs Of Functions.
