The function f(x) is a quadratic function of the form
f(x) = ax2 + bx + c
The exploration is carried out by changing the parameters a, b and c included in f(x) above.
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, parameter b to zero and parameter c to a non zero value; f(x) is a constant function. Compare the graph of f(x) in blue and that of - f(x) in red. Explain.
3 - Keep the value of a equal to zero, select non zero values for b to obtain a linear function . How can the graph of h(x) be obtained from that of f(x)? (Hint: compare the positions of points (x,f(x)) and (x,-f(x)) )
4 - Select a non zero value for a to obtain a quadratic function . Compare the two graphs and explain the reflection of the graph of f(x) in the x-axis.
How can the graph of -f(x) be obtained from that of f(x)?
More on reflections:
Reflection Of Graphs In y-axis.
Reflection Of Graphs Of Functions.