In this challenge we will write several **procedures** to graph different mathematical equations on screen using Python Turtle.

We will focus on:

- Linear equations:
*y = ax + b* - Quadratic equations:
*y = ax*^{2}+ bx + c - Trigonometric functions: e.g.
*y = cos(x)*

#### (x,y) coordinates using Python Turtle?

On the Python trinket used below the turtle screen is 400 pixels wide by 400 pixels high.

Look at the canvas below to understand how

**(x,y) coordinates**work:

#### Linear Equation

y = ax + b

A linear equation produces a straight line when graphed on screen.

**Your task:**

Change the **parameters** used when calling the *drawLine()* **procedure** to graph the following equations:

- y = 2x + 60
- y = -x + 10
- y = x
- y =
^{1}/_{2}x

#### Quadratic Equation

y = ax

^{2}+ bx + cAdd another **procedure** called *drawQuadraticEquation()* that will take three **parameters**: a, b and c and be used to graph and display the matching quadratic equation.

Use this new procedure to graph the following equations:

- y = x
^{2}+ 2x + 60 - y =
^{1}/_{2}x^{2}– 3x + 20 - y = x
^{2} - y = -x
^{2}+ 100

#### Trigonometric Functions

You can now add further procedures to draw the main trigonometric functions. To do so you will need to import the math library using an import statement.

1 |
import math |

Here are the three main functions you will need to implement:

- cosine: y = cos(x)
- sine: y = sin(x)
- tangent: y = tan(x)