Solves "line meets curve" and simultaneous problems visually, with no algebra. Works the same way on every model - graph both functions, then use the calculator's own intersect tool.
In short: The intersection of two graphs is a point where both functions give the same output, so its coordinates solve the equation f(x) = g(x). On a GDC you graph both functions and use the intersect tool at each crossing. Use it for simultaneous equations, line-meets-curve questions and break-even problems.
When you'd use this
Solving simultaneous equations graphically - when a question says "solve graphically" or "using your GDC," or when the algebra would be too messy to do by hand.
"Line meets curve" questions - finding where a straight line crosses a quadratic, exponential, trig or other curve.
Checking an algebraic answer - solve the pair of equations by hand, then confirm the same coordinates come up graphically.
Break-even and comparison problems - e.g. "when does cost equal revenue," or "when do two phone plans cost the same," where each quantity is its own function of the same variable.
Solving f(x) = k - graph y = f(x) and y = k as a second, horizontal line, and find where they intersect.
Comparing two models - e.g. two different growth or decay functions - to find when one overtakes the other.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
TI-84 Plus CE
Casio fx-CG50 and fx-CG100
TI-Nspire CX
Key sequence
2nd → CALC → 5:intersect, move near the crossing, then press ENTER three times.
Press G-Solve (SHIFT F5) → Intersection (ISCT).
menu → Analyze Graph → Intersection.
On a TI-84 Plus CE
From the home screen, press Y= to open the equation editor.
Clear any old functions - move the cursor onto a line and press CLEAR.
Next to Y1=, type your first function. Use the X,T,θ,n key for x (not ALPHA+X). Press ENTER.
Next to Y2=, type your second function the same way. Press ENTER.
Press GRAPH to draw both curves.
If nothing appears, or the graphs don't overlap: press WINDOW and set Xmin/Xmax/Ymin/Ymax to cover where the curves should cross, or press ZOOM → 0:ZoomFit.
Press 2nd → CALC → 5:intersect.
The screen asks "First curve?" - press ENTER. "Second curve?" - press ENTER again. "Guess?" - move the cursor close to the crossing point and press ENTER a third time.
The coordinates of that intersection are shown at the bottom of the screen.
To find another crossing point, repeat the last two steps with your guess near that point.
Tip: Adjust the window/zoom so every intersection point is visible before using the tool - the intersect finder only looks near where your cursor is.
On a Casio fx-CG50 / fx-CG100
From the main menu, press MENU and select Graph (or press the Graph icon).
Clear any old functions - highlight a line and press DEL.
Press SHIFT → F3 (TYPE) and check the graph type is Y= (the default). Type your first function next to Y1 and press EXE.
Type your second function next to Y2 and press EXE.
Press F6 (DRAW) to plot both curves.
If nothing appears, or the graphs don't overlap: press SHIFT → F3 (V-Window) to set a sensible range, or press Zoom (F2) → Auto.
Press SHIFT → F5 (G-Solve) → Intersection (ISCT).
If there's more than one crossing, use the ◄ ► arrow keys to move between them.
The coordinates of the intersection appear at the bottom of the screen.
Move to each remaining crossing point with the arrow keys, or re-run G-Solve, to read off the rest.
Tip: If G-Solve doesn't find a crossing, check your V-Window covers the x-range where the graphs actually meet.
On a TI-Nspire CX
From the home screen, open a new Graphs page: press ctrl + I → Add Graphs (or select the Graphs app icon).
In the entry line at the bottom (f1=), type your first function and press ENTER.
Click the entry line again for f2=, type your second function, and press ENTER. Both curves plot automatically.
If nothing appears, or the graphs don't overlap: menu → Window/Zoom → Window Settings to set a sensible range, or Zoom → Zoom-Fit.
Press menu → Analyze Graph → Intersection.
Click just to the left of the crossing point, then click just to the right of it, to bound the search.
The intersection is marked on the graph and its coordinates are shown.
Repeat menu → Analyze Graph → Intersection, bounding a different crossing, for each remaining point.
Tip: Bound the search tightly around one crossing at a time - with several intersections close together, a wide bound can pick the wrong one.
Here's a real IB-style question that uses exactly this technique.
MediumCalculatorPaper 2[4 marks]
The curve C has equation y = x² − 2x, and the line L has equation y = x + 4.
Find the coordinates of the points where C and L intersect.
(−1, 3) and (4, 8)
Mark it
Correct4 / 4 marks
Worked solution & mark scheme:
M1 Graph Y1 = x² − 2x and Y2 = x + 4
M1 Use the intersect tool at each crossing point
A1 Correct point (−1, 3)
A1 Correct point (4, 8)
Common questions
When would I need to find where two graphs meet in IB Maths?
The intersect tool solves "line meets curve" and simultaneous-equation problems visually, with no algebra. Solving simultaneous equations graphically, when a question says "solve graphically" or "using your GDC", or when the algebra would be too messy to do by hand. "Line meets curve" questions: finding where a straight line crosses a quadratic, exponential, trig or other curve.
How do I find where two graphs meet on a TI-84 Plus CE?
1. Enter both functions as Y1 and Y2 and graph them. 2. 2nd → CALC → 5:intersect, move near the crossing, then press ENTER three times. 3. Repeat for each crossing point.
How do I find where two graphs meet on a Casio fx-CG50 and fx-CG100?
1. Enter both functions as Y1 and Y2 and graph them. 2. Press G-Solve (SHIFT F5) → Intersection (ISCT). 3. Repeat for each crossing point.
How do I find where two graphs meet on a TI-Nspire CX?
1. Enter both functions as Y1 and Y2 and graph them. 2. menu → Analyze Graph → Intersection. 3. Repeat for each crossing point.
What should I watch out for when I find where two graphs meet?
Adjust the window so the crossing point is on screen first - the solver looks near the part of the graph you can see.
How are marks awarded when I find where two graphs meet in an IB exam?
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Graph Y1 = x² − 2x and Y2 = x + 4; M1: Use the intersect tool at each crossing point; A1: Correct point (−1, 3); A1: Correct point (4, 8).
