Calculus >

The**roots of a function**, sometimes called the

*zeros of a function*, are any points where the input (x) produces a result (y) of zero. In other words, it’s where the function or graph crosses the x-axis. It takes seconds to find the roots of a function graphically on the TI-89 graphing calculator.

## Roots on the TI 89: Example 1

**Sample problem: **Find the roots of the following function graphically on the TI-89:

f(x) = x^{2} – 8x + 15

Step 1: Press the HOME key.

Step 2: Press the diamond (♦) key, then press F1 to enter into the y=editor. Press ENTER once to navigate to the input line at the bottom of the screen.

Step 3: Step 3: Press x ^ 2 – 8 x + 1 5 to enter the function into the “y1=” slot.

Step 4: Press the Enter key.

Step 5: Press the diamond (♦) key, then press F3 to view the graph of the function.

Step 6: Press the F5 key and then press 2 to select “Zero” (which is short for *zeros of a function*).

Step 7: Arrow to the left of the x-intercept for the “Lower Bound” and then press the ENTER key.

Step 8: Arrow to the right of the x-intercept for the “Upper Bound,” and then press the Enter key.

The TI-89 will return a value of 3 for “x” and 0 for “y” This means that one of the roots for the function is 3.

Step 9: Repeat steps 6 through 8. However, for the “Lower Bound,” arrow to a point that is to the **right **of the first intercept and then press the ENTER key. For the “Upper Bound,” arrow to the right of the x-intercept and press ENTER. The TI-89 will return a value of 5 for “x” and 0 for “y” This means that the other root for the function is 5.

*That’s it!*

**Tip**: Use the zoom function to see the graph more clearly on the screen. The zoom function is the F2 key when you are viewing the graph. Press 2 to Zoom In or press 3 to Zoom Out.

## Roots of a function on the TI-89: Example 2

**Sample problem:** Find the roots of the following function using the table feature on the TI-89:

f(x) = x^{2} – 7x + 12

Step 1: Press the Home key.

Step 2: Press the diamond key and then press F1 to enter into the y=editor.

Step 3:Press Enter to go down to the input line.

Step 4: Press x ^ 2 – 7 x + 1 2 to enter function into the “y1=” slot.

Step 5: Press Enter.

Step 6: Look to the left of the Y1 slot to make sure there is a check mark next to the function. If there isn’t a check mark, press the F4 key.

Step 7: Press the diamond key and then F5 to view the table of values for this function.

Step 7: Find what the variable “x” is equal to when “y1” is equal to zero on the table. Use the up and down scroll keys to scroll through the table. You should find that the x-values 3 and 4 satisfy this condition. These are the roots of this function.

*That’s it! You’re done!*

**Tip**: The table of values you generate will contain values for each checked function, so make sure you only have a check mark next to the function you want to draw a table for.

If you prefer an online interactive environment to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

*Facebook page*and I'll do my best to help!