1. Lesson 2

1.8. Explore 4

Mathematics 20-2 M3 Lesson 2

Module 3: Quadratics


tip

Here is a way to help you remember that domain is all possible x-values and range is all possible y-values. Write x and y in alphabetical order, and write domain and range in alphabetical order.

  • x, y
  • domain, range

Another way to describe a quadratic function and its parabolic graph is by its domain and range. Recall that the domain is all possible x-coordinates on the graph. The range is all possible y-coordinates on the graph.

 

In the quadratic function y = ax2 + bx + c, the domain is all possible values of x and the range is all possible values of y.

 

If you were to project a “shadow” of a graph onto the y-axis, the resulting interval corresponds to the range of the relation. If you project a “shadow” of a graph onto the x-axis, the resulting interval corresponds to the domain of the relation.

 

Try This 2
 

The Domain and Range applet allows you to see the “shadow” that the domain of the relation casts on the horizontal axis and the “shadow” that the range of the relation casts on the vertical axis.

 

 

This is a screenshot for Domain and Range.

 

Use the applet to answer the following questions. Note: The shadows for the domain and the range are different colours. The shadow tells you the domain and the range of each relation.

  1. Select the “Circle” graph. Slide the domain slider down to the bottom to see the shadow.

    1. How would you express the domain of the circle in words?

    2. How would you express the domain of the circle in symbols?

    3. Express the range of the circle in words and in symbols. (You can move the “Range Shadow” slider all the way to the left to see the range shadow.)

    Answer

  2. Now de-select the “Circle” graph, and select the “Quadratic 1” graph.

    1. When the quadratic 1 function is written in standard form, would the value of a be greater than or less than zero? How do you know?

    2. What is the domain of the Quadratic 1 function?

    3. What is the range of the Quadratic 1 function?

    Answer

  3. Now de-select the “Quadratic 1” graph, and select the “Quadratic 2” graph.

    1. When the Quadratic 2 function is written in standard form, would the value of a be greater than or less than zero? How do you know?

    2. What is the domain of the Quadratic 2 function?

    3. What is the range of the Quadratic 2 function?

    Answer