 # Graphing Calculator | Derivative Graphing Calculator | Intercepts

The world's most advanced Online Graphing Calculator, deploying the most sophisticated Cartesian and Polar coordinate systems, with which you can construct polar and parametric graphs by animation to see how they are traced; alsograph with axes rotated too!

Advanced Online Graphing Calculator for graphing function, equation (with variables on both sides) and parametric curve. This intelligent graphing calculator automatically detects the type of expressions and graphs as you type using this syntax in the Cartesian or polar coordinate systems. This sophisticated graphing calculator is the world's first and the only known graphing tool that lets you animate polar and parametric graphs to visualize how they are traced and constructed from start to end. Other easy-to-use features of this graphing calculator allow you to find all the x-intercepts (zeros or roots of functions) on a bounded interval with a single click and label axes with π or any number. This function and parametric derivative calculator finds and also graphs derivatives. Full instruction

• This Graphing Calculator, with many unique features, can be used to graph functions, equations and parametric curves using the Cartesian and polar coordinate system.
• Trace polar and parametric graphs by pressing the Animate button. This Polar Graphing Calculator and Parametric Graphing Calculator are the only graphing tools that show you how these types of graphs are constructed from start to end.
• Calculate the x-intercepts (zeros or roots) of a function.
• Graph derivatives of functions and parametric equations.
• This unique Graphing Calculator is the only graphing tool that lets you rotate axes to graph in non-perpendicular coordinate systems.
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Polar Transparent
Axis
Label

Rotation°

Angle Mode RAD DEG GRD
Graph Thickness

To copy or save graphs right click on the image of a saved graph below and select "Copy" or "Save image..." from the pop-up menu.

Try the all-in-one Calculator: Graphing calculator, matrix calculator, complex number calculator, derivative calculator

## Introduction: Graphing Calculator

This intelligent graphing calculator detects the type of expressions (function, equation and parametric expressions) and graphs as you type in the Cartesian or polar coordinate system on an interval (domain).

• f(x) = 3x2 + 2x + 1 (function)
• x^3-xy+2y^2 = 5x+2y+5 (equation)
• p(t) = [sin(t), cos(t)] (parametric curve)

Using this graphing calculator you can easily find all the x-intercepts of (the graph of) a function on an interval by solving the equation f(x) = 0.

Another useful feature of this graphing calculator allows you to calculate derivatives of functions and parametric equations and graph derivatives.

• The quickest way to type dom= (-∞, ∞) is by deleting the domain entirely (including dom=). You'll need to press Enter on the keyboard if Graph as you type is not enabled.
• To graph a piecewise-defined function or parametric curve use the multi-graph window. Enter each piece with the corresponding sub-interval as a single function or parametric curve.
• To find the intersection of two functions f(x) and g(x), enter the expression f(x) - g(x) and press Solve to calculate the x-intercepts of f(x) - g(x), which are the x-coordinates of the points of intersections of f(x) and g(x).
• This graphing calculator can show you how the polar graph of a function or the graph of a parametric curve is drawn by pressing the Animate button.
• This graphing calculator also has the ability to graph in non-perpendicular coordinate system. You can rotate axes and graph expressions.

Interesting curves: Select an expression below to graph it using the Cartesian or polar coordinate system. For best results you may need to select Graph Fineness as "+1" or higher.

Functions

Lines

1 x+1 2x

Semi-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))
Functions – Polar

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)
Equations

Lines

y = 1 x = 1 y = x+1 x = y+1 3x + y = 2 3x - y +5 = 4x+2y-2

Circles

x^2+y^2 = 9 (x-2)^2 + (y-2)^2 = 4

Ellipses

x^2/4 + y^2/9 = 1 x^2-xy+2y^2-x-2y-8=0

Parabolas

y=x^2 y = x^2-4x+4 2x^2-4xy+2y^2-x-2y-2=0

Hyperbolas

x^2/4 - y^2/9 = 1 24x^2-50xy-49y^2+97x+93y-164=0

Other graphs

x^2 = y^2 sin(xy) = cos(xy)
Equations — Polar
Currently, not available.
Parametric

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)
Parametric – Polar

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)]