Graphing Calculator

Plot mathematical functions on an interactive graph. Supports polynomials, trig, log, and custom functions.

Drag to pan. Scroll to zoom. Hover for coordinates.

How to Use This Calculator

Plot the parabola y = x² - 4. Enter "x^2 - 4" in the function field, set X Min = -5, X Max = 5, Y Min = -5, Y Max = 10, then click Plot. The graph shows a U-shaped parabola crossing the x-axis at x = -2 and x = 2 (the roots), with its vertex at (0, -4). Now try a sine wave: enter "sin(x)" with X Min = -10, X Max = 10. The graph shows the classic wave oscillating between -1 and 1, crossing zero at every multiple of π. You can drag to pan — click and hold anywhere on the graph, then move your mouse. Scroll to zoom in and out — this is useful for examining the behavior near specific points, like the root of a function. Try "x^3 - 3*x" and zoom in around x = 1 to see the local minimum.

About Graphing Calculator

This interactive graphing calculator plots mathematical functions on a coordinate plane. Enter any function of x using standard mathematical notation and see its graph instantly. Supported operations include addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and functions like sin(), cos(), tan(), log(), ln(), sqrt(), abs(), and more. The graphing calculator is an essential tool for students studying algebra, calculus, trigonometry, and physics. It helps visualize function behavior, identify roots, intercepts, asymptotes, and turning points. You can adjust the view window by setting X and Y axis ranges, or interactively pan and zoom using mouse drag and scroll. Whether you are analyzing a simple linear function or a complex rational expression, this tool provides clear visual insight into mathematical relationships.

How to Interpret Your Results

Roots & Intercepts: Points where the blue curve crosses the x-axis are the real roots (where f(x) = 0). For f(x) = x² - 4, the roots at x = -2 and x = 2 are clearly visible. The y-intercept (where x = 0) is at y = -4. For f(x) = sin(x), roots occur at x = ..., -2π, -π, 0, π, 2π, ...

Behavior at Extremes: As x → ±∞, a polynomial's end behavior is determined by its leading term. For f(x) = x³ - 3x, as x → ∞, f(x) → ∞ (the graph goes up to the right), and as x → -∞, f(x) → -∞ (the graph goes down to the left). This is visible on the graph's left and right edges.

Discontinuities: For functions like 1/x or tan(x), the graph shows vertical asymptotes where the function is undefined. Try plotting "1/x" with ranges -10 to 10. You'll see the curve shoot toward +∞ as x approaches 0 from the right, and toward -∞ as x approaches 0 from the left.

Frequently Asked Questions

Can I plot multiple functions on the same graph?

Currently, the calculator plots one function at a time. To compare functions, you can plot one, note key features, then plot the other. For example, plot "x^2" to see a parabola, then plot "x^2 - 4" to see it shifted down by 4 units. The overlapping mental comparison helps understand transformations like vertical shifts.

How do I find the intersection of two graphs?

Since the calculator plots one function at a time, find intersections by setting the two functions equal and solving algebraically. For example, to find where x² = x+2, solve x² - x - 2 = 0, which gives x = -1 and x = 2. Plot each function separately and verify these x-values are where they cross.

What is the difference between linear and quadratic graphs?

Linear functions (f(x)=mx+b) produce straight lines with constant slope. Quadratic functions (f(x)=ax²+bx+c) produce parabolas that curve and have a single vertex. A linear graph crosses the x-axis at most once, while a quadratic can cross twice, once (tangent), or not at all, depending on the discriminant.

How do I adjust the viewing window?

You can adjust X Min, X Max, Y Min, and Y Max in the input fields before plotting. You can also interactively pan by clicking and dragging on the graph, and zoom by scrolling up (zoom in) or down (zoom out). The input fields update automatically as you pan and zoom.

Can I graph inequalities?

The calculator currently plots functions as curves, not shaded inequality regions. However, you can graph the boundary function of an inequality. For y > x², plot "x²" to see the boundary parabola. The solution region would be all points above that curve, which you'd need to visualize mentally.