GDC workflow: graph, intersect, read
Big idea: Technology helps you find the intersection accurately.
Your job is to enter the graphs correctly, choose the intersection tool, and report the answer in the form the question wants.
| Step | What to do |
|---|---|
| 1 | Enter the first equation as Y₁ |
| 2 | Enter the second equation as Y₂ |
| 3 | Graph both equations |
| 4 | Open the intersect tool |
| 5 | Answer First curve?, Second curve?, Guess? |
| 6 | Read and round the answer correctly |
What IB wants: If the question asks for the solution of simultaneous equations, give the coordinate point.
If it asks you to solve one equation graphically, give the x-values.
IB-style question — solve an equation with the GDC [4 marks]
Use technology to solve the equation 3x + 4 = 0.5x² + 1, giving your answers correct to three significant figures.
Step by step
- Enter each side as its own graph so you can use the intersect tool.
- A parabola and a line meet in at most two points, so run 5:intersect at each crossing.
- The calculator gives the two x-values; round each to 3 significant figures.
Final answer
x = 6.87 or x = −0.873 (3 s.f.). Because the question asks to solve the equation, give the x-values only.
Choosing a good viewing window
If you cannot see it, you cannot solve it: A poor graph window can hide the intersection or make the graph too squashed to read accurately.
| Problem on screen | What to try |
|---|---|
| Graphs are cut off | Widen the x-range or y-range |
| Everything is squashed | Use a smaller scale |
| No intersection is visible | Zoom out or recenter near the crossing |
| Only one crossing is visible | Check whether another crossing is outside the window |
IB trap: If the question asks for all solutions, do not stop after finding the first visible intersection.
Check the full relevant domain.
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Reading and rounding calculator output
Worked example
The calculator gives the intersection point (2.381, 5.762).
Report the solution to 3 significant figures.
Step by step
- Round the x-coordinate to 3 significant figures.
- Round the y-coordinate to 3 significant figures.
- Write the coordinate pair in the correct order.
Final answer
(2.38, 5.76)
Common mistake: Do not swap the coordinates.
The calculator gives x first, then y.
When there is more than one intersection
One graph pair can have several solutions: A line and a curve can meet more than once.
Technology helps you find each intersection, but you must remember to report all relevant solutions.
Worked example
A calculator shows intersections at x = −1 and x = 3.
The question asks for all solutions.
What should you write?
Step by step
- The word all means every relevant intersection is needed.
- Write both x-values as solutions.
Final answer
x = −1 and x = 3
Do not stop too early: After finding one intersection, scan the graph or use the intersect tool again near another crossing.