How to Find X and Y Intercepts on the TI-84 Evo

The TI-84 Evo can tell you exactly where a graph crosses each axis, down to the coordinates, instead of leaving you to read them off the picture. The work happens in the CALCULATE menu: one command reads the y-intercept, another hunts down every x-intercept.

Start with a graph on the screen

You need the function graphed before you can find its intercepts. For this walk-through we'll use Y1 = X² − X − 6: type it into the Y= list and press graph. If entering and drawing a function is new to you, the full walk-through is in how to graph a function on the TI-84 Evo.

A parabola graphed on the TI-84 Evo, crossing the x-axis on both sides of the origin and dipping below it

You can see the curve cross the y-axis once and the x-axis twice. Now let's get the exact numbers.

Find the y-intercept

The y-intercept is where the curve crosses the y-axis, and that always happens where x is 0. So finding it just means asking the calculator for the height of the graph at x = 0.

  1. Open the CALCULATE menu. Press 2nd then trace (the blue CALC label sits above the trace key). The menu lists the things the Evo can measure on a graph.
    The TI-84 Evo CALCULATE menu listing value, zero, minimum, maximum, intersect
  2. Choose 1: value and enter 0. The graph comes back with an X= prompt at the bottom. Type 0 and press enter. The cursor jumps to the point where the curve meets the y-axis and shows X=0, Y=−6, so the y-intercept is (0, −6).
    The TI-84 Evo showing X equals 0, Y equals negative 6, the y-intercept marked on the parabola

Find the x-intercepts

The x-intercepts are where the curve crosses the x-axis, where y is 0. You may also hear them called the zeros or the roots. The Evo finds them with the zero command, one at a time.

  1. Open CALCULATE again and choose 2: zero. Press 2nd then trace, arrow down to zero, and press enter. The status bar reads Left Bound?: a graph can cross the axis more than once (this one does it twice), so you fence in the intercept you want, starting with a spot on its left.
  2. Walk the cursor past the left x-intercept. Hold down the left arrow (or tap it) to slide the cursor along the curve; the X= readout at the bottom updates as you go. Stop once the cursor sits just left of the intercept (around x = −2.1 here) and press enter.
    The TI-84 Evo asking Left Bound with the cursor walked to x equals negative 2.1, just left of the x-intercept
  3. Set the right bound and confirm. At Right Bound?, arrow back a few presses so the cursor sits on the other side of the intercept and press enter. At Guess? press enter once more, and the Evo lands exactly on X=−2, Y=0.
    The TI-84 Evo showing Zero, X equals negative 2, Y equals 0, the left x-intercept marked
  4. Do the same for the right x-intercept, with a shortcut. At any bound prompt you can type an x-value instead of arrowing, and the cursor jumps straight there. From the graph you can tell this one sits somewhere between x = 0 and x = 5, so run zero again, type 0 and press enter for the left bound, then 5 and enter for the right bound, and press enter once more. This time the answer is X=3, Y=0. The two x-intercepts are (−2, 0) and (3, 0).
    The TI-84 Evo showing Zero, X equals 3, Y equals 0, the right x-intercept marked

Good to know

  • Bracket one intercept at a time. A parabola can meet the x-axis twice, once, or not at all, and zero only reports the one inside your bounds. Any value between the two intercepts, like the 0 we used here, works as the inner edge for both of them.
  • Every answer lands in Ans. The status bar says the result was stored to Ans, so you can pull the last intercept straight into another calculation with 2nd then (-).
  • The same menu finds the vertex. Where zero and value live, so do minimum and maximum. Bracketing the dip of this parabola with minimum returns its turning point, (0.5, −6.25).
  • Prefer a table? If you'd rather read an intercept off a column of numbers, see how to make a table of values on the TI-84 Evo.