Explore our free online **Cartesian** and **polar** **graphing calculator**, a powerful tool for graphing the most common types of mathematical expressions: **functions**, **equations** (including implicitly defined functions), **parametric curves** (also known as parametric equations), and **points**.

**Graphing a function** `f(x)`

and additionally finding its x-intercepts? And what about finding symbolic derivatives for solving a calculus problem, determining where the graph is increasing or decreasing, and where itâ€™s concave up or down? Or perhaps you want to graph the function in the polar coordinate system, compare it to its Cartesian graph, and be fascinated by the step-by-step creation of polar graphs? This powerful Cartesian and polar graphing calculator is not just made for these purposes, but it allows you to graph other types of mathematical expressions: **equations in two variables**, and **parametric equations** in addition to **point sets**.

## 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)*

Unique among graphing calculators, it provides the remarkable capability of **rotating each axis** independently. This advanced feature makes it the world's only graphing tool (besides other graphers developed by this site) that allows graphing in **oblique coordinate systems**, alongside Cartesian & polar coordinate systems.

Additional Features:

**Unique Polar Parametric Graphing Calculator:**This graphing tool, as a parametric equation graphing calculator, is the only one that can produce polar parametric graphs.**Unmatched Animation Capability:**Users can visualize the step-by-step formation of polar and parametric graphs. When graphing in the polar coordinate system, it's also the only graphing tool that shows the radial axis rotating while animating polar graphs of functions and parametric curves.**Calculus Tools:**Beyond graphing, it can also find the**x-intercepts**(also known as**zeros**or**roots of a function**), and even calculate**symbolic derivatives**of**functions**and**parametric**expressions and graph them, making this graphing calculator a powerful tool for solving problems in Calculus.

In particular, you can use this graphing calculator to:

- Graph
**linear functions**and**linear equations**in**point-slope**form and**slope-intercept**form. - Graph
**conic sections**in the standard form such as`(x-h)^2 + (y-k)^2 = r^2`

, and the general form (`Ax^2 + Bxy + Cy^2 - Dx + Ey + F = 0`

), which can be a**circle**,**ellipse**,**parabola**,**hyperbola**, or some degenerate graphs. - Graph
**level curves**, which are in the form`F(x,y) = c`

.

**Lines**

**Semi-circles**

**Semi-ellipses**

**Parabolas**

**Semi-hyperbolas**

**Other graphs**

**Lines**

**Circles**

**Spirals**

**Roses**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Cardioids**

**Limacons**

**Lemniscates**

**Butterfly curve**

**Lines**

**Circles**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Other graphs**

**Lines**

**Circles**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Other parametric graphs**

**Butterfly curve**

**Lines**

**Circles**

**Spirals**

**Roses**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Cardioids**

**Limacons**

**Lemniscates**

**Other parametric graphs**

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

**pi**is replaced by.`π`

**..t**is replaced by. (You can also use`θ`

`x`

or`t`

; they are internally replaced by`θ`

).**inf**(**infinity**) is replaced by.`∞`

**MouseMatics**: Find out how to use your mouse to rotate axes, change scales, and translate coordinate systems.