Equivalent quadratic expressions
Reading information
about a function from correspondence rules
The table below presents four correspondence rules for four
functions. One of the correspondence rules is written in
Product Form, another in Vertex Form,
another in Polynomial Form, and yet another in a different form.
|
|
|
|
What information does each form reveal about the function?
|
|
Write correspondence rules in each of the different forms for each of the functions.
|
|
Below each of the correspondence rules you wrote, indicate which of the following properties of the functions can be gleaned from the correspondence rule without a need for calculation:
- The form of the graph: Does the quadratic function have a minimum or a maximum?
- The point of intersection with the x-axis.
- The point of intersection with the y-axis.
- Points of intersection with other straight lines.
- The position of the function's vertex.
- The domain where the function's values are positive and the domain where they are negative.
- The domain where the function is increasing and the domain where it is decreasing.
- Information about the function's rate of change.
|
|
|
|
A different form
|
Polynomial Form
|
Vertex Form
|
Product Form
|
|
|
|
(f(x)=(x-3)(x-5 |
|
|
g(x)=3(x-1)²-27 |
|
|
h(x)=-2x²-20x-42 |
|
|
| k(x)=6-(x+1)(x-3)/2 |
|
|
|
|
|
|
