Graphing Calculator
Type a function such as x^2 - 4 or sin(x) and this graphing calculator draws it at once, with up to six curves on one set of axes. Zoom and pan the view, switch trig between radians and degrees, and open Show the work for the y-intercept and, for a line or parabola, the slope, vertex and roots. It plots functions y = f(x) only.
Last updated November 4, 2026
2 functions plotted, x from -10 to 10, y from -10 to 10: y = x^2-4; y = sin(x). Arrow keys pan the view, plus and minus zoom, 0 resets.
Drag to pan. Pinch, or hold Ctrl or Cmd and scroll, to zoom. With the graph focused: arrow keys pan, + and - zoom, 0 resets.
- Function 1: y = x^2-4
- Function 2: y = sin(x)
Result
2 functions plotted
y = x^2-4; y = sin(x)
Trig in radians. Gaps in a curve mean the function is undefined there.
Show the work
Formula: y = f(x), sampled across the x range and joined point by point. For degree 2: a = (f(1) + f(-1)) / 2 - f(0), b = (f(1) - f(-1)) / 2, c = f(0); vertex x = -b / (2a); D = b^2 - 4ac; roots x = (-b ± sqrt(D)) / (2a).
- Function 1: f(x) = x^2-4. View: x from -10 to 10, y from -10 to 10.
- Y-intercept: f(0) = -4, so the graph crosses the y-axis at (0, -4).
- Polynomial of degree 2 detected from f(0) = -4, f(1) = -3 and f(-1) = -3, then checked at x = 2, -3 and 0.5: a = (-3 + -3) / 2 - -4 = 1, b = (-3 - -3) / 2 = 0, c = -4.
- Vertex: x = -b / (2a) = 0, y = -4, so the vertex is (0, -4).
- Discriminant: D = b^2 - 4ac = 16.
- Roots (x-axis crossings): x = -2 and x = 2.
- Sample points across the x range: f(-10) = 96; f(-5) = 21; f(0) = -4; f(5) = 21; f(10) = 96.
Result: y-intercept -4; roots -2, 2
How a function is plotted
y = f(x)
The x range is cut into several hundred equal steps. At each x the calculator works out y = f(x) and joins neighboring points with short straight lines. Where f(x) has no value, such as 1/x at 0, ln(x) for x of 0 or less, or sqrt(x) for negative x, the line stops and starts again, so a gap means the function is undefined there.
If two neighboring points are far apart vertically, the interval between them is halved again and again. A steep but continuous curve such as x^2 near the edge stays joined. A true jump, such as tan(x) at pi/2 or 1/x at 0, never shrinks, so the curve breaks there and no line crosses the asymptote.
For a line y = mx + b, m is the slope and b the y-intercept. For a parabola y = ax^2 + bx + c, the vertex is at x = -b / (2a), the discriminant is D = b^2 - 4ac, and the roots are x = (-b ± sqrt(D)) / (2a): two real roots if D is positive, one if zero, none if negative. These appear only when the function is a polynomial of degree two or lower, fitted from f(0), f(1) and f(-1) and checked at three more points.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Trigonometry Calculator and Integral Calculator.
Supported syntax
Write the variable as x. A leading y = or f(x) = is ignored. Supported: polynomials with + - * / and ^ and brackets (2x + 1, x^3 - 2x); sin, cos, tan, asin, acos and atan; exponentials such as e^x and 2^x; ln (natural) and log (base 10); sqrt, cbrt and abs; and the constants pi and e.
Multiplication can be left out: 2x, 3(x+1) and 2sin(x) are understood. Functions need brackets, so write sin(x), not sin x. Up to 200 characters.
Gaps and asymptotes
sqrt(x) starts at 0 with nothing to its left, and ln(x) is defined only above 0. 1/x splits into two branches, and tan(x) shows a separate branch between each pair of asymptotes. An expression that cannot be read, such as 2+ or foo(x), shows an error under its own row and is skipped while the others still plot.
Zoom, pan and keyboard controls
Type limits into X min, X max, Y min and Y max, or use the buttons: Zoom in halves each range, Zoom out doubles it, the arrows move the view by a tenth, and Reset view returns to -10 to 10. Each span must be from 0.000001 to 1,000,000,000.
On the graph, drag to pan and pinch to zoom. With a mouse, hold Ctrl or Cmd and scroll, or click the graph first. From the keyboard, tab to the graph, then use arrow keys to pan, + and - to zoom and 0 to reset.
What it does not do
Only y = f(x) is graphed. There are no implicit curves such as x^2 + y^2 = 25, no equations with y on both sides, no parametric or polar curves, no derivatives and no intersection points.
How to use the Graphing Calculator
- Type a function in the Function 1 box, for example x^2 - 4, and press Add function for more curves (up to six).
- Fix any row showing an error; it is skipped.
- Set X min, X max, Y min and Y max, or drag, pinch or use the zoom and arrow buttons.
- Choose radians or degrees if you use sin, cos or tan.
- Open Show the work for the y-intercept, and for a line or parabola the slope, vertex and roots.
Worked example: y = x^2 - 4
This parabola has a = 1, b = 0 and c = -4. The y-intercept is f(0) = -4, the vertex is at x = 0 so it is (0, -4), and D = 0 - 4 × 1 × (-4) = 16. The roots are (0 ± 4) / 2, so x = -2 and x = 2.
| x | y | Meaning |
|---|---|---|
| -3 | 5 | left arm |
| -2 | 0 | root |
| 0 | -4 | vertex, y-intercept |
| 2 | 0 | root |
| 3 | 5 | right arm |
Frequently asked questions
Why does my curve have a gap or stop suddenly?
The function has no value there: square roots of negatives, logarithms of zero or negatives, division by zero and tan at 90 degrees are undefined, so the line breaks.
How many functions can I plot at once?
Up to six. Each gets its own color and line pattern, solid or dashed, so you can tell them apart without relying on color.
Can I graph a circle or an equation with y on both sides?
No. Only y = f(x) is supported, so x^2 + y^2 = 25 is rejected. Draw a circle as two functions, y = sqrt(25 - x^2) and y = -sqrt(25 - x^2).
Does it use radians or degrees for sin and cos?
Radians by default, so sin(pi/2) is 1. Switch the angle unit to degrees and sin(90) is 1 instead. It applies to every function.
Why are the roots and vertex missing in Show the work?
They are reported only for lines and parabolas. For sin(x) or x^3 you get the y-intercept and a table of sample points, with a note saying so.