Explore graphical representations of the most common types of mathematical expressions — functions, equations with two variables, parametric equations, and point sets — with our world's most powerful, easy-to-use graphing calculator.
Our online graphing calculator is a sophisticated and feature-rich graphing software application for drawing the graphs of functions, equations (including implicitly defined functions), parametric curves and points in the Cartesian and polar coordinate systems.
Here are some examples of syntax:
- f(x) = x^2sin(x) + 2x + 1 (function)
- x^3-xy+2y^2 = 5x+2y+5 (equation)
- p(t) = [sin(t), cos(t)] (parametric)
- 1,2; -2, 2/3; sin(π/3), 2^3-1 (points)
It can easily find the roots of a function (also known as zeros or x-intercepts), and also calculate symbolic derivatives of functions and parametric curves and graph the derivatives.
This graphing calculator has features that enable you to animate the graphing process in a unique way that helps you understand it better. It is also unique in its ability to visualize graphs in an oblique coordinate system where each axis can be rotated independently. These features provide an interactive and engaging way to explore mathematical concepts and enhance your understanding of graphing.
In particular, you can use this graphing calculator to:
- Graph conic sections in the standard and the general form (
Ax^2 + Bxy + Cy^2 - Dx + Ey + F = 0), which can be a circle, ellipse, parabola, hyperbola, or some degenerated graphs. - Graph level curves, which are in the form
F(x,y) = c. - Solve equations to find x-intercepts (zeros or roots) of a given function.
- Calculate and graph the symbolic derivatives of the 1st and 2nd order of a given function or parametric expression.
Lines
1 x+1 2xSemi-circles
√(9-x^2) -√(9-x^2)Semi-ellipses
√(9-x^2/3) √(9-x^2/3)Parabolas
x^2 0.5x^2-4x+1 -(0.5x^2-4x+1)Semi-hyperbolas
√(x^2-4) -√(x^2-4)Other graphs
√(4sin(2x)) √(4cos(2x))Lines
2csc(θ) 2sec(θ) 1/(sin(θ) - cos(θ))Circles
1 2 6sin(θ) 8cos(θ)Spirals
θ θ/5 dom=(0, 10π) √(θ) dom=(0, 10π) 1/θ dom=(0, 10π)Roses
4sin(3θ) 4sin(2θ) 4sin(5θ) 4sin(4θ)Ellipses
1/(1-.8cos(θ)) 1/(1-.8sin(θ)) 1/(1+.8cos(θ)) 1/(1+.8sin(θ))Parabolas
1/(1-sin(θ)) 1/(1+cos(θ)) 1/(1+sin(θ)) 1/(1-cos(θ))Hyperbolas
1/(1+2cos(θ)) 4/(1+2sin(θ)) 1/(1-2cos(θ)) 4/(1-2sin(θ))Cardioids
3+3cos(θ) 2+2sin(θ) 3-3cos(θ) 2-2sin(θ)Limacons
2+3cos(θ) 1+2sin(θ) 2-3cos(θ) 1-2sin(θ)Lemniscates
√(4sin(2θ)) √(4cos(2θ))Butterfly curve
e^sin(θ)-2cos(4θ)+sin((2θ-π)/24)^5 dom=(0, 12π)Lines
y = 1 x = 1 y = x+1 x = y+1 3x + y = 2 3x - y +5 = 4x+2y-2Circles
x^2+y^2 = 9 (x-2)^2 + (y-2)^2 = 4Ellipses
x^2/4 + y^2/9 = 1 x^2-xy+2y^2-x-2y-8=0Parabolas
y=x^2 y = x^2-4x+4 2x^2-4xy+2y^2-x-2y-2=0Hyperbolas
x^2/4 - y^2/9 = 1 24x^2-50xy-49y^2+97x+93y-164=0Other graphs
x^2 = y^2 sin(xy) = cos(xy)Lines
[t, 1] dom=(-5, 5) [1,t] dom=(-5, 5) [t, 2t] dom=(-5, 5)Circles
[4sin(t), 4cos(t)] [3sin(t)+1, 3cos(t)+1]Ellipses
[4cos(t), 3sin(t)] [3cos(t), 4sin(t)] [4sin(t), 3cos(t)] [3sin(t), 4cos(t)]Parabolas
[t, t^2] dom=(-4, 4) [t^2, t] dom=(-4, 4)Hyperbolas
[3sec(t), 4tan(t)] [3tan(t), 4sec(t)]Other parametric graphs
[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]Butterfly curve
[sin(t)(e^cos(t)-2cos(4t)-sin(t/12)^5), cos(t)(e^cos(t)-2cos(4t)-sin( t/12 )^5)] dom=(0, 12π)Lines
[2csc(t), t] [2sec(t), t] [1/(sin(t) - cos(t)), t]Circles
[1, t] [2, t] [6sin(t), t] [8cos(t), t]Spirals
[t, t] [t/5, t] dom=(0, 10π) [√(t), t] dom=(0, 10π) [1/t, t] dom=(0, 10π)Roses
[4sin(3t), t] [4sin(2t), t] [4sin(5t), t] [4sin(4t), t]Ellipses
[1/(1-.8cos(t)), t] [1/(1-.8sin(t)), t] [1/(1+.8cos(t)), t] [1/(1+.8sin(t)), t]Parabolas
[1/(1-sin(t)), t] [1/(1+cos(t)), t] [1/(1+sin(t)), t] [1/(1-cos(t)), t]Hyperbolas
[1/(1+2cos(t)), t] [4/(1+2sin(t)), t] [1/(1-2cos(t)), t] [4/(1-2sin(t)), t]Cardioids
[3+3cos(t), t] [2+2sin(t), t] [3-3cos(t), t] [2-2sin(t), t]Limacons
[2+3cos(t), t] [1+2sin(t), t] [2-3cos(t), t] [1-2sin(t), t]Lemniscates
[√(4sin(2t)), t] [√(4cos(2t)), t]Other parametric graphs
[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]
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