Thank you for using Quick Graph and voting it as the best graphing calculator available on the AppStore! It is a powerful, high quality, graphic calculator that takes full advantage of the multitouch display and the powerful graphic capabilities of the iPad and iPhone, both in 2D and 3D. A simple, yet intuitive interface that makes it easy to enter and/or edit equations and visualize them in mathematical notation. It's capable of displaying explicit and implicit equations as well as inequalities in both 2D and 3D, in all standard coordinate systems: cartesian, polar, spherical and cylindrical, all with amazing speed and beautiful results, which can be copied, emailed or saved to the photo library.

Even though all the standard features that made Quick Graph a great app are free, you can opt to unlock additional features (below, via in-app purchase). Upgrading Quick Graph to unlock the additional features will not only enhance your user experience, but it will also support the developing of Quick Graph!

Quick Graph+ differs from the free Quick Graph in that it already includes the advanced feature set which gives you access to all the features, such as implicit graphs and tracing.

The keyboard of Quick Graph on the iPhone or the iPad has the following math operators, variables, constants and functions, that can be used to plot 2D and 3D Graphs and calculation (see Figure 1):

** Operators:**

+ Plus |
- minus |
* Multiplication |
/ Division |

√ ntnh root |
^ Power |
() Parentheses |
, Parameter Separator |

; Expression separator |
< Less than |
> Greater than |
= Equality and assignment |

Note: roots should be typed as (degree)√(expression), square root is a special case, where you can enter 2√x or √x, as long as there’s no expression to the left of the √ symbol (except for an operator).

x, y, z, r, Θ, Φ

π, e

** functions:**

sin: sine |
cos: cosine |
tan: tangent |

cot: cotangent |
sec: secant |
csc: cosecant |

asin: arc sine |
acos: arc cosine |
atan: arc tangent |

sinh: hyperbolic sine |
cosh: hyperbolic cosine |
tanh: hyperbolic tangent |

coth: hyperbolic cotangent |
csch: hyperbolic cosecant |
sech: hyperbolic secant |

d/dx: x derivative |
d/dy: y derivative |
d/dz: z derivative |

ln: natural logarithm |
log: base 10 logarithm |
log2: base 2 logarithm |

abs: Absolute Value |
ceil: next closest integer |
floor: previous closest integer |

If(condition, true, false) | max | min |

mod: remainder function |
todeg: to degrees |
torad: to radians |

When you first start the application a window similar to these will appear:

Now for the fun part, press the add button (the one that looks like a plus sign) and let’s start writing our first equation! You should see a keyboard similar to this (figure 4):

Notice how next to the field to enter the expression,there is an icon that will allow you to browse the library of prebuilt equations. As you will learn later, QuickGraph also has a library that will allow you to save your own equations for future use. If you can’t see the icon,simply erase the equation from the field and tap on the library icon. You will see something like figure 5 but withyour own library. You can select or delete any equation from the library.

*Its important to notice that you have to enter the evaluation point first and then the equation, separated by a semicolon (;) x=3 ; 7x+4*

An expression is a group of numbers, operators, variables, and functions or a combination ofthese elements. Now, go back to the new equation view, to plot a function simply enter: y=x^2 and tap the done button. If the expression contains an error, a message under the expression will appear describing it.

An expression is a group of numbers, operators, variables, and functions or a combination ofthese elements. Now, go back to the new equation view, to plot a function simply enter: y=x^2 and tap the done button. If the expression contains an error, a message under the expression will appear describing it.

You can use trigonometric functions, inequalities, and a set of prebuilt functions that we will explore in depth in subsequent sections, for example y

The upgraded version also allows you to trace the graph by tapping and holding. A line will appear showing the intercepts with the graph (figure 11).

You can change the color of the graph by selecting the edit option (second icon) and tap on the little color bullet to the right of the expression. (figure 12).

Now, to erase equations (graphs), go to the edit view on the iPhone or to the equations view on the iPad, then simply click on the edit button or swipe across the graph you want to delete.

In the edit view, you also have the possibility of turn on/off the equation, via the visibility icon:

The library button opens a view where you can add your expressions to the library (if not already there) and can delete or select an equation to graph (figure 14)

The help button displays the application’s credits and a way to contact us, for queries or suggestions. (figure 16).

In 2D Quick Graph has the ability to calculate roots and intercepts of cartesian equations, just press the gray plus triangle on the top right during tracing and it will show you the options to calculate and display roots and intercepts. This can take a few seconds if many equations are plotted at the same time.

Quick Graph also lets you see a table of values for the current graphed equations. Scroll down to the top to see the limits and interval options. Tap on an equation to zoom on it.

to the top to see the limits and interval options. Tap on an equation to zoom on it.

The settings button enables you to personalize Quick Graph for certain functionalities:

- Autohide toolbar (iPhone only): If you would like to have more room for visualization, the toolbar can be hidden, and it will appear again by tapping the bottom of the screen.
- Keyboard Clicks: Turns on/off the clicking sound of the application keyboard.
- Enable shakes: Allows you to shake your device to reset the view and to clear the text field in the add expression view.
- Use random color: if enabled, every time a graph is added, it will be given a random color.
- Default color: The default color for the graphs, if random color is turned off.
- Reset library: Erases the library (2D and 3D) and restores the original equations.

- Dark background: Sets the background to black.
- Thick Lines: Graphs will be displayed using a thicker 2 pixel line.

- Rotation box: Enable/disable the rotation box.
- Light Background: Change the background color of the 3D view to white.
- Display Values: Displays the current values for the x, y and z axis.
- Faster implicits: Turning off faster implicits will allow the use of a more complex algorithm to calculate implicit surfaces. The result will be a smoother surface, but it will require more time to calculate the graph (see graphs 28 and 29).

The last option in settings is the Optional Features. Figure 20-3 shows the option to unlock the advanced options.

The 3D view functionality is similar to the 2D view. However, there are some differences. For instance, instead of moving the graph by dragging you can rotate it. Also, if you want to move the graph you will need to drag two fingers.
In figure 21 we can see the basic 3D view with its axis if you zoom in or zoom out, the equation will be recalculated with the new limits determined by the bounding box.

Entering an equation in 3D is the same as in 2D (the same interface figure 22). Quick Graph will automatically give you messages if there is any error in the equation and a little marker will be set where the error can be found.

One great functionality is that you can solve symbolic derivatives by tapping the plus button that appear under the equation when it contains a derivative (figure 23).

The visualization of 3D equations is shown in figures 24 to 26. With double tap you can change the visualization mode, from points to wireframe to a solid surface.

The basic version will allow you to graph up to 6 equations. The enhanced version will allow you to graph unlimited equations (well, almost... there is still a limitation imposed by the available memory in your device).

** We encourage you to purchase the enhanced version to support
the development of Quick Graph.**