TI 89 Calculus > How to use the Zeros Function TI-89

In calculus, you will be asked to find the **zeros of a function** — sometimes called the roots of a function. The zeros of a function are the point(s) where the input (x) produces a result (y) of zero. Use the Zeros Function on the TI-89 to find roots (or zeros) easily. The expression on the calculator is zeros(expression,var) where “expression” is your function and “var” is the variable you want to find zeros for (i.e. x or y variables).

## Zeros function on the TI 89 Steps

**Example problem 1:** Find the zeros of this function: f(x) = x^{2} – 10x + 16

Step 1:Press the **F2** key from the **HOME **screen and then press the number **4 **button. This combination of buttons selects the “zeros” command.

Step 2: Press the following keys to enter the function into the command line: x ^ 2 – 1 0 x + 1 6, x )

Step 3: Press the **ENTER **key.

The resulting zeroes for this rational function will appear as a notation: ( 2 , 8 ) This means that the zeroes of this function are at x = 2 and x = 8.

That’s it! You’re done!

**Tip**: If you are asked to use the zeros function on the TI 89 to find **zeros for a certain interval**, set the interval using the “with” operator (a vertical slash |), the inequality operator (press the green diamond and then 0) and the “and” operator (+). For example, if you wanted to find the zeros of the equation sin(2x) – 3cos(x) between the interval 0 and 2π, the input would be:

zeros(sin(2x)-3cos(x),x)|0≤ and x≤2π

## More Examples

**Example problem 2: **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 3

**Example problem 3:** 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.

Source: Prentice Hall.