A free online graphing calculator for New Zealand students, teachers, and professionals. Plot up to six equations simultaneously, zoom and pan the coordinate plane, trace exact coordinates, and generate tables of values. Supports all standard functions used in NCEA Mathematics Levels 1, 2, and 3 including polynomials, trigonometry, exponentials, and logarithms. No sign-up, no download, no cost.
Type any equation using x as the variable into one of the equation fields on the left. Press Enter or click away and the graph will appear immediately. You can plot up to six equations at once, each in a different colour so you can compare them easily.
To zoom in or out, use the scroll wheel on your mouse, pinch on a touchscreen, or click the Zoom + and Zoom - buttons. To pan (move the viewing window), click and drag the graph in any direction. To reset to the standard view showing x and y from -10 to 10, press Reset View.
Trace mode locks the cursor to the nearest plotted curve and shows the exact x and y coordinates as you move along it. This is useful for finding where a function crosses an axis or reaches a turning point.
The Table button generates a table of (x, y) values for all active equations over any x range and step size you choose. This is helpful for identifying patterns and checking specific values.
The calculator accepts standard mathematical notation. Use * for multiplication, / for division, and ^ for powers. Here are the supported functions:
sin(x), cos(x), tan(x), asin(x), acos(x), atan(x) for trigonometry. sqrt(x) for square root. abs(x) for absolute value. log(x) for base-10 logarithm. ln(x) for natural logarithm. x^2 for x squared. e for Euler's number (2.718...). pi for pi (3.14159...).
A common NCEA Level 1 task is to graph a straight line and a parabola on the same axes and find where they intersect. For example, to find where y = x + 2 meets y = x² - 4, enter both equations and zoom in on the crossing points. The x-coordinates of the intersections are the solutions to x² - x - 6 = 0, which factorises to (x - 3)(x + 2) = 0, giving x = 3 and x = -2. Use the Trace tool to confirm this visually.
At NCEA Level 2, students work with graphs of the form y = a sin(bx + c) + d. Try plotting y = 2*sin(x) to see a sine wave with amplitude 2. Then plot y = sin(2*x) to see the period halved. Comparing both on the same axes makes the effect of each parameter immediately visible, which is the kind of analysis NCEA questions ask you to describe.
At NCEA Level 3 and first-year university, you will work with functions like y = e^x (exponential growth), y = ln(x) (natural log), and polynomials up to degree four. Try plotting y = x^3 - 3*x to see a cubic with two turning points. The local maximum and minimum are where the derivative equals zero, which you can locate visually using the Trace tool.
A Texas Instruments TI-84 Plus costs between $150 and $220 in New Zealand. The TI-84 Plus CE, which is colour and approved for NCEA examinations, costs around $200. While a physical calculator is required in formal NCEA exams, an online graphing calculator is ideal for homework, study, understanding concepts, and checking your answers before an exam. This tool runs entirely in your browser with no download, no account, and no cost.
For reference, the NCEA-approved graphing calculators include the Texas Instruments TI-84 Plus, TI-84 Plus CE, TI-Nspire CX, Casio fx-9750GIII, Casio fx-9860GIII, and Casio ClassPad II. This online calculator is for study and homework purposes and is not permitted in formal NCEA examinations, which require an approved physical device.
Press Enter to apply an equation. Press + and - to zoom in and out. Press R to reset the view. Press T to toggle trace mode. Hold Ctrl (or Cmd on Mac) and scroll to zoom faster.
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