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Function f(x) used 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.
Interactive Tutorial
- click on the button above "click here to start" and MAXIMIZE the window obtained.
- Use the sliders to set parameter a to zero, parameter b to zero and parameter c to a positive value; f(x)is a constant function. Compare the graph of f(x) in blue and that of h(x) = |f(x)| in red. Change c to a negative value and compare the graphs again. Use the definition of the absolute value functions to explain how can the graph of |f(x)| be obtained from the graph of f(x).
- 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: use the definition of the absolute value functions and reflection of a graph on the x-axis.
- Set b and c to zero and select a positive value for a to obtain a quadratic function . Why are the two graphs the same? (Hint: use the definition of the absolute value functions).
- Set b and c to zero and select a negative value for a to obtain a quadratic function . Why are the two graphs reflection of each other? (Hint: use the definition of the absolute value functions and reflection of a graph on the x-axis).
- Keep the values of a and b as in 5 above and change gradually c from zero to some positive values. How can the graph of h(x) be obtained from that of f(x)?
- Select different values for a, b and c and explore.
Exercises
Sketch the following functions
- f(x) = | x - 1 |
- g(x) = | x2 - 4 |
- h(x) = | -x |
You will find more pages in this web site related to absolute value functions and equations.
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