Online graphing calculator

The graphing calculator draws functions of x on a coordinate grid. You can enter up to 20 expressions, and each gets its own color. Examples that work:

• Polynomials: x^3 − 4x, 0.5x^2 + 2x − 1
• Trig: sin(x), 2cos(3x), tan(x), sec(x)
• Exponentials and logs: exp(x), 2^x, ln(x), log(x)
• Roots and absolute value: sqrt(x), cbrt(x), abs(x − 2) or |x − 2|
• Rational functions: 1/x, (x + 1)/(x − 2)
• Steps and factorials: floor(x), round(x), x!

You can drop the multiplication sign (2x, ax, 3sin(x)) and write y = or f(x) = at the start if you like. If an expression can't be read, for example because of a missing parenthesis, the field is flagged right away and the other curves keep working. Angles are in radians.

Any single letter other than x and e is treated as a parameter, and a slider appears for it as soon as you type it. Write y = a·sin(b·x) and you get sliders for a and b; drag them and the curve updates instantly. Each slider starts at 1 with a range from −10 to 10, and you can change the min and max to zoom in on the values you care about.

Sliders are the quickest way to see what each number in a formula does:

• y = a(x − h)^2 + k: h moves the parabola left and right, k up and down, and a makes it narrower, wider or upside down.
• y = m·x + b: m tilts the line, b moves it up and down.
• y = a·sin(b·x + c): a is the amplitude, b changes the period (2π/b) and c shifts the wave.

The same letter means the same value in every expression, so you can share a parameter between curves.

Scroll the mouse wheel over the graph, or pinch on a phone or tablet, to zoom around the point under your finger or cursor. Drag to move the view. The + and − buttons zoom around the center, and Reset returns to x from −10 to 10 and y from −6 to 6. The current range is shown under the graph.

Tips:

• For trig functions, a range of about −6.3 to 6.3 (−2π to 2π) shows two full periods.
• Near vertical asymptotes, as with 1/x at 0 or tan(x) at π/2, the curve is broken instead of drawing a false vertical line.
• Points where the function is undefined (ln of a negative number, for example) are simply left out.
• Zoom in on a crossing point to see it more precisely; the key points are recalculated for the visible range.

The calculator marks the notable points of every curve in the visible range and lists them in a table:

• Zeros, where a curve crosses the x-axis;
• Maxima and minima, the local turning points;
• Intersections of any two curves.

Use the checkboxes to show or hide each type. The points are found numerically: the visible range is sampled densely and every candidate is refined to about ten significant digits. That is accurate enough to check homework. A point where a curve only touches the axis, such as x^2 at 0, is listed both as a zero and as a minimum.

Plot y = x^2 − 2 and y = x. Algebraically the curves cross where x² − 2 = x, that is x² − x − 2 = 0, which factors to (x − 2)(x + 1) = 0.

1. Enter x^2 − 2 as the first expression and x as the second.
2. The graph marks two intersections, and the table lists them as (−1, −1) and (2, 2).
3. It also marks the zeros of the parabola at x ≈ ±1.414214 (±√2) and its minimum at (0, −2).

To solve quadratics exactly, with the discriminant and vertex shown, use the quadratic formula calculator.

The table of values lists every curve at 11 points, from the start value you choose in steps of your choice, which is handy for checking homework or sketching by hand. If a function is undefined at a point, the table says so.

Everything you enter, the expressions, the slider settings and the view, is saved in the page address. Copy the link or use the Share button, and whoever opens it sees exactly the same graph. All drawing and calculation happen in your browser, and nothing is uploaded. For single calculations, the scientific calculator is quicker.