Find where two graphs meet
Find the point where two curves cross, such as y = x² and y = x + 2.
The solutions of f(x) = g(x) are the x-values where the two graphs cross. Graph both and use the calculator to find the crossing point.
The parabola y = x² and the line y = x + 2 meet at (-1, 1) and (2, 4). The steps below find (-1, 1).
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Enter X² on y=, press down, enter X + 2 on the next line, then press graph.
y=X,T,θ,nx²▼X,T,θ,n+2graphOpen the CALC menu (2nd then trace) and pick 5, intersect. Press enter to accept the first curve, enter again for the second.
2ndCALCtrace5enterenterType a guess near the crossing you want, -2, and press enter.
(−)2enter
You should seeIntersection X=⁻1 Y=1
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
In the Graph app enter X² and X + 2 on two lines (press EXE after each).
MENU3X,θ,Tx²EXEX,θ,T+2EXEDraw with F6, open G-SOLV (F5) and press F5 for INTSECT.
F6F5F5
You should seeINTSECT X=-1 Y=1
Press the right arrow to jump to the next crossing, (2, 4).
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
On the graphs page, type x^2, press down (not enter), type x + 2 and press enter.
docxx²▼x+2enterOpen the menu, choose 4, Analyze Graph, then 4, Intersection.
menu44
You should seeintersection x=-1. y=1.
Tips
- A guess helps the calculator choose which crossing to find when there are several.
- If the graphs cannot be seen crossing, change the window first.