Castle Learning Reference

Calculator Tips for Pre-Calculus

Finding the x-intercepts, Roots or Zeros of a Graph

The following instructions apply to a TI83 or TI84 graphing calculator.

First place the equation into 'y₁=' and graph the equation. Then adjust the window so that all the x-intercepts are shown on the screen.

Key strokes:

'2^nd'
'trace'
Arrow down to 'zeros' and hit enter or just hit '2'.
Right arrow or left arrow over to the x-intercept
The calculator is asking for the 'left bound?'.

To help decipher the left bound from the right bound, use the following.

- Left bound - will be above the x-axis if the graph is decreasing in range values (has a negative slope) from the left to the right at the point of intersection with the x-axis. The left bound will be below the x-axis if the range values are increasing from left to right at the point of intersection with the x-axis.

- Once the cursor is in the correct location close to the intersection point, hit Enter.
The calculator is now asking for the 'right bound?'

To help decipher the left bound from the right bound, use read the following.

- Right bound - will be above the x-axis if the graph is increasing in range values (has a positive slope) from the left to the right at the point of intersection with the x-axis. The left bound will be below the x-axis if the range values are decreasing from left to right at the point of intersection with the x-axis.

- Once the cursor is in the correct location close to the intersection point, hit Enter.
The calculator says 'Guess?' Hit enter.

At the bottom of the screen, you will now see:

The 'x' value is the root, zero or x-intercept. The 'y' value will always be zero at an x-intercept.

**If you see a 'y' value containing an 'E', don’t worry. It is scientific notation and means that the value is equal to zero.

**After you hit Enter when the calculator is at 'Guess': If you see the message 'Err:bound', you made a mistake with the left and right bounds. You must start over again.