# Calculus path.

Module: Functions / Equations

### Introduction to functions

In Mathematics, an equation is a statement that shows two things are equal. For example: 10 = 5 x 2, is an equation, as both sides of the equals sign are equal to 10.Click here to read more.

### Find the equation from a scenario

Sometimes we will have some information about a problem & will need to create the equation to solve the problem. In the below, we have worked through two examples, one for finding the equation for costing the manufacture of a box & one for the equation for total mileage used across two vehicles with different miles per gallon figures.Click here to read more.

### Find the piecewise equation of a line

Given the below chart, we need to figure out the equation for the line. We will use the piecewise method, where we split the line into chunks & define each part of the line using the formula y – y1 = m(x – x1) where:Click here to read more.

### Find the Slope Intercept (y = mx + b) equation of a line

Let’s say we have been given two points of a line. One is (1,2) and the other is (3,5). Using this & the formula y = mx + b, we can define the equation for the line.First, we need to calculate m (the slope). We do this by taking y change divided by x change. This gives us 3/2. We can then inject this into the formula to make y = 3/2 x + b. Click here to read more.

### Understanding Parabolas

A parabola is a symmetrical graph that models the trajectory of something being thrown. You can imagine looking at the below, we throw a ball & it arches in a relatively symmetrical fashion.A parabola has a number of defining features. Firstly, we have the vertex, which is the maximum or minimum point on the graph, depending which way up it is (opened upwards or opened downwards). Click here to read more.