Find the zeros (roots) of a graph
Find where a curve crosses the x-axis. The example is y = x² − 4, with zeros at x = -2 and x = 2.
A zero of a function is an x-value where y = 0, so the graph touches or crosses the x-axis there.
The calculator needs to know roughly where to look. On some models you give a left and right boundary around the zero. On others you move the cursor close first.
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 − 4 on y= and press graph.
y=X,T,θ,nx²−4graphOpen the CALC menu (2nd then trace) and pick 2, zero.
2ndCALCtrace2Left bound: type 0 and press enter. Right bound: type 5 and press enter. Then press enter for the guess.
0enter5enterenter
You should seeZero X=2 Y=0
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.
Draw X² − 4 in the Graph app.
MENU3X,θ,Tx²−4EXEF6Open G-SOLV (F5) and press F1 for ROOT. It shows the left zero first.
F5F1Press the right arrow to see the other zero.
▶
You should seeROOT X=2 Y=0
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.
Draw the graph on the graphs page, then press the right arrow to move the cursor towards the zero on the right.
docx^2▶−4enter▶Open the menu, choose 4, Analyze Graph, then 1, Zero.
menu41
You should seezero x=2. y=0.
Tips
- If a zero is not found, the curve may not cross the axis in that range. For example x² + 1 never reaches zero.
- To find the other zero, give bounds around it instead.
Related guides
- Find a maximum or minimumFind the lowest or highest point of a curve, such as the vertex of y = x² − 2x.
- Solve a quadratic equationFind the roots of x² − 5x + 6 = 0 with a polynomial solver or the quadratic formula.
- Make a table of valuesList x and f(x) side by side for a function, starting wherever you like.