To use the Desmos graphing calculator, open the official calculator, enter an equation in the expression list, and adjust the graph window until the useful part is visible. Then add another equation, inspect intersections, or make a table to check individual values. You can start graphing without signing in.
The examples below use a line and a parabola with simple, independently checked answers. They show how to tell whether your entry, your viewing window, or your interpretation needs attention. Keep the calculator open beside this guide so you can change one thing at a time.
How do you enter your first equation?
In a blank expression line, type y=3x-2. Desmos draws the line as you enter it. Press Enter to add another expression, then type (2,4). This point belongs on the line because 3 × 2 − 2 = 4. Parentheses and the comma make this an ordered pair rather than an arithmetic expression.
Next, enter y=x^2 on its own line. The caret introduces the exponent, so this means x squared. You now have a straight line and a parabola. If your input looks unfamiliar after typing, read the formatted expression before changing the window. A missing exponent or minus sign creates a different graph.
The color icon beside an expression toggles that graph on and off. Temporarily hide the individual point if it makes the crossing harder to see. Desmos documents expression entry and selecting important points in its getting-started guide.
Why is the graph missing or cut off?
A viewing window is only the rectangle of the coordinate plane currently on screen. Drag the graph paper to move it, or use the zoom controls to show more or less. Open Graph Settings to enter explicit lower and upper bounds for the axes.
For this example, try x from −3 to 4 and y from −4 to 10. Those bounds include the line’s y-intercept at (0, −2), the parabola’s vertex at (0, 0), and both intersections. They are suggested bounds for these equations, not a universal setting for every problem.
If you instead enter y=(x-30)^2+100, its vertex is (30, 100), well outside that suggested window. An apparently empty screen would not mean the equation has no graph. Resetting to Default Viewport can undo an accidental pan, but distant features still need suitable bounds. The Graph Settings documentation explains viewport and axis controls.
How do you find and check intersections?
Select a curve, then hover over an available gray point of interest to reveal its coordinates. Select the point to keep its label visible. For y=3x-2 and y=x^2, the crossings are (1, 1) and (2, 4). Each ordered pair satisfies both equations.
Check the first point by substituting x=1: the line gives 3 × 1 − 2 = 1, and the parabola gives 1² = 1. At x=2, both give 4. Algebra explains why there are two: setting the expressions equal gives x² − 3x + 2 = 0, which factors as (x − 1)(x − 2) = 0.
A decimal coordinate on another graph may be rounded. Use it as a numerical approximation unless you have independently established an exact value. Also inspect the wider graph before concluding there is only one crossing. A tight window can hide a second intersection without changing the equations.
How do you plot a table of points?
Choose Add Item, then Table. In the first two columns, enter these x and y pairs: (−2, 4), (−1, 1), (0, 0), (1, 1), and (2, 4). These values come from squaring each x. They should lie on y=x^2, making the table a useful check on both the plotted curve and your data entry.
Each row represents one point. Entering 2 in the x column and 4 in the y column creates (2, 4); swapping them creates (4, 2), which is not on this parabola. If the table’s points are outside the window, use Zoom Fit to bring the data into view.
A table of five points does not establish every point on a curve. Connecting them with straight segments also does not reproduce the parabola between them. Keep the equation visible when comparing the discrete samples with the full curve. See Desmos’s table instructions for table styling and additional options.
How do you restrict the domain?
To show only part of the line, change its expression to y=3x-2 {0<=x<=2}. The restriction permits x values from 0 through 2, including the endpoints. The resulting segment runs from (0, −2) to (2, 4). Type the condition inside curly braces at the end of the equation.
Changing the viewing window does not impose this mathematical restriction. If you zoom out, an unrestricted line continues beyond the earlier screen edges; the restricted segment still stops at its endpoints. This distinction matters when a model applies only during a specified time interval or across a limited distance. Desmos’s restriction guide covers conditions on x and y.
How should you save and use the result?
Use Save to keep your work in an account. For sharing, the current Desmos user guide distinguishes a snapshot from a saved graph link: a snapshot preserves the shared state, while the saved link can reflect later saved changes. Choose the version that matches what a classmate or teacher should see.
Use graphing when the question concerns curves, intersections, or how values change across a domain. A scientific calculator is often enough for evaluating a numerical expression; a two-point slope calculator answers a narrower rate-of-change question. Before submitting a graph, check equations, axis bounds, restrictions, and any requested units. For trigonometric work, check the radians/degrees setting too.
A small whiteboard can make substitution checks easy to revise beside your laptop. If you need one, browse small graph-grid dry-erase boards on Amazon. Paper works equally well for these examples.
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