In Lesson 1.1 you defined the function f(x) = 2x² – 5x – 3 and found its zeros with Guess and Check and by factoring. In Lesson 1.2 you graphed the function and found its zeros graphically. In this lesson you will represent the function numerically with a table and use the table to find the zeros.

Creating a Table of Function Values

To make a table of values for a function, you need to enter the function in the Y= Editor. You should have already done this in Lesson 1.1.

• Make sure f(x) is still stored in Y₁ by pressing to view the Y= Editor.

Displaying the Table Setup Screen

Before you view the table, you should set its parameters.

• View the Table parameters, which are displayed in the Table Setup screen, by pressing [TBLSET], which is above the graphing key.

Table Setup Parameters TblStart and Tbl

The value in TblStart will be the first value of x in the table.

• Enter -1 next to TblStart to set the beginning x-value in the table at -1.

The value in Tbl determines how much x increases from one row to the next in the table. This value should be 1. Match the other settings in the figure shown below.

• View the table of values of f(x) = 2x² - 5x - 3 for x = -1, 0, 1, 2, 3, 4 and 5 by pressing [TABLE], which is above the graphing key.

Finding Zeros from a Table

The table provides numerical evidence for two zeros. One zero must exist between x = -1 and x = 0 because the corresponding values in Y₁ change sign and the function is continuous, i.e., there are no breaks in its graph. The other zero is x = 3 because the corresponding value of Y₁ is 0.

You can get a better approximation of the zero between -1 and 0 by changing Tbl to 0.1.

• Return to the Table Setup screen by pressing [TBLSET].
• Change the value of Tbl to 0.1.
  You can move up and down within the Table Setup screen with the cursor movement keys .

• Press [TABLE] to view the new Table values.

This method of decreasing Tbl between two values in the table is called table zoom.

1.3.1 What zero is shown in the table above? Click here for the answer.

Summarizing

For r a real number, the following statements are equivalent:

1. r is a zero (or root) of the function f
2. r is an x-intercept of the graph of the function f
3. x = r is a solution to the equation f(x) = 0
4. (x - r) is a factor of the polynomial f(x)