Graph a Cubic Function
A cubic function such as y = x³ − 3x has an S-shaped graph with up to three roots and up to two turning points; for y = x³ − 3x they are at (−1, 2) and (1, −2).
At a glance
| What it is | Graph cubic functions online and find their roots, turning points and inflection point. Example: y = x³ − 3x. Free graphing calculator. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| General form | y = ax³ + bx² + cx + d |
|---|---|
| Roots | Up to 3 real roots (at least 1) |
| Turning points | Up to 2, where the slope 3ax² + 2bx + c = 0 |
| Example: y = x³ − 3x | Roots 0 and ±√3 ≈ ±1.732; local max (−1, 2); local min (1, −2) |
| End behavior (a > 0) | Falls to −∞ on the left, rises to +∞ on the right |
What shape is a cubic graph?
y = x³ always increases and flattens out at the origin, its inflection point. Adding an x term, as in y = x³ − 3x, creates a hill and a valley before the curve continues upward.
A negative leading coefficient flips the graph: it rises on the left and falls on the right.
How to use it in Plotline
- The graph of y = x³ − 3x together with y = x³ is already loaded above. Edit the equation in the list to change it.
- Drag the graph to move around, scroll or pinch to zoom, and tap the crosshair to reset the view.
- Hover over or tap the curve to read the coordinates of any point.
- Press Enter to add another equation and compare graphs in different colors.
Frequently asked questions
How many roots can a cubic have?
A cubic always has at least one real root and at most three. y = x³ − 3x has three: x = −√3, 0 and √3.
Is it free?
Yes. The graphing calculator is free with no account and no sign-up: plot as many equations as you like, use sliders, save graphs in your browser and share them by link. It installs as an app and keeps working offline.
Learn more
Related
- Parabola (quadratic) – Graph quadratic functions y = ax² + bx + c online.
- Linear equation – Graph linear equations y = mx + b online.
- Reciprocal function (1/x) – Graph y = 1/x online and see its two branches and asymptotes at x = 0 and y = 0.
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