2.2 Graphical Modelling

Click here to access the recommended Learning Plan for this topic

Learning objectives

Learn how to use quadratic, cubic, exponential, simple trigonometric (sine or cosine), and simple hyperbolic (rare but possible) to model different situations
A learner could use algebraic method or a combination of graphical transformations to model situations

The modelling process is referred as below

Under the M(model) J(justification) F(Fit), a student should be able to demonstrate how to model a particular function with sounded mathematical method (e.g. using algebra with points given to obtain expected equations), justify with their features of equations, and can check if their equations (models) meet the requirements using algebra

Here is an example link with notes and further explanations for MJF!

How should we model using a quadratic or cubic or simple trig or exponential function given two points?

Function Transformations

No matter what function you learn about, you can always apply the same transformations!

For the function f(x):

Left/Right Translation: f(x+a)

Up/Down Translation: f(x) + a

Amplitude (Vertical Stretch): a*f(x)

Frequency of Oscillations (Horizontal stretch): f(a*x)

Maths is Fun - Function Transformations

Task to do (student desmos activity): What is My Transformation? Parangula

Functions, domain and range

L2 Graphical methods: Domain and range

It is important to understand "function" in maths.

Applying the understanding of domain and range on Desmos, we could create specific graphs we are aiming for.

Quadratic functions

Learn the difference between the 3 quadratic forms

Standard Form y = ax^2 + bx + c
Vertex Form y = a(x+b)^2 + c
Root Form / Intercept Form = a(x+b)(x+c)

Particularly for the Vertex and Root Forms, make sure you know how to:

Draw the graph from the equation
Write down the equation from the graph

3 Quadratic Forms - Geogebra Interactive Tool

Graphing in vertex, intercept and standard forms

Vertex form questions to practice

There are quadratic questions provided below. It is very important to go through lots of questions to integrate your understanding of sketching quadratic equations using different forms and transformations.

Textbook practice material

L2 Graphical methods-quadratics