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How to find where two graphs cross on a TI-84 Plus CE, TI-84 Plus or TI-83 Plus

By E-Code · updated

Graph both functions, press 2nd CALC (above TRACE) and 5 for intersect, then ENTER for the first curve, ENTER for the second curve, and type a guess near the crossing and press ENTER. The calculator shows the X and Y where the two graphs meet.

Before you start

Type both functions into the Y= editor first: this guide uses Y1 = X² and Y2 = X + 2 (Y=, X,T,θ,n, x², ENTER, X,T,θ,n, +, 2, then 2nd QUIT).

Y= X,T,θ,n X² ENTER X,T,θ,n + 2 2nd MODE

Step by step

  1. Draw both graphs. GRAPH Press GRAPH. Y1 = X² and Y2 = X + 2 are already typed in for you.
  2. Open CALC. 2nd TRACE Press 2nd, then TRACE. CALC (written above TRACE) holds the graph tools.
  3. Pick intersect. 5 Press 5 for intersect. It asks for the first curve; the cursor is on Y1.
  4. Pick the first curve. ENTER Press ENTER to pick Y1. The cursor jumps to the next graph, Y2, by itself.
  5. Pick the second curve. ENTER Press ENTER to pick Y2. Now it asks for a guess.
  6. Guess near a crossing. 3 Type 3. The graphs cross twice; a guess near X = 2 picks the right-hand crossing.
  7. Find the crossing. ENTER Press ENTER. The calculator homes in on where the two graphs meet.
  8. Read the point. X = 2, Y = 4: 2² = 4 and 2 + 2 = 4. Do it again with a guess of −2 to find the other crossing, (−1, 1).

What the screen shows

X = 2, Y = 4: 2² = 4 and 2 + 2 = 4. Do it again with a guess of −2 to find the other crossing, (−1, 1).

Look for X=2 on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-84 calculator and each key lights up in turn as you press it.

Try “Find where two graphs cross” on the TI-84 calculator

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