Week 8- Properties Of Quadratic Functions

This week we started learning about quadratic functions and their properties associated with them. What is a quadratic function?

A quadratic function can be mathematically defined to be y=ax^2+bx+c and what makes this function a quadratic? It’s degree of 2, in fact algebraically speaking, any equation, polynomial expression, function etc that can be identified as a quadratic simply means that it’s highest degree is 2.

What kinds of properties are associated with quadratic functions:

Firstly, the graph of a quadratic function will always result in a parabola (resembles a “U” shape either opening up or down), a parabola is always semetrical and will always contains vertex (either a minimum or maximum value), and an axis of symmetry (refer to vocabulary list below).

When talking about the properties of quadratic function you can also note the translation as well as the scale factor/value.

Translation examples:

y=x^2+7

This parabola will translate vertically upwards 7 “points”

y=(x-2)^2

This parabola will translate horizontally 2 “points” to the RIGHT  (note: horizontal translation often moves opposite to the direction you expect).

The scale factor/value refers to the parabola being either stretched or compressed across the graph and it will become either taller/skinnier or wider/droopier, this is affected by the value of  “a” and corresponds also to its congruency, “is it congruent?” refers to wether or not the graphing pattern is still 1,3,5, if there is any sort of stretch or compression, it is not congruent.

Scale factor/value example:

y=3x^2

This parabola will become taller/skinnier.

Extra vocabulary:

vertex: the point where both sides of the parabola join together

minimum: the parabola opens upwards, the vertex is identified as the minimum value

maximum: the parabola opens downwards, the vertex can be identified as the maximum value

axis of symmetry: a line that can be imagined to run through the very center of the parabola (through the vertex) parallel to the y axis, imagine that it slices the parabola into two identical “mirror image” type pieces.

 

Leave a Reply

Your email address will not be published. Required fields are marked *