Topic

The Standard and Vertex forms for quadratic functions

Team members

Names:  Azan Peermohamed                                                                                                                                  

 Overview

This section is about quadratic functions.  The two forms of the quadratic equation that the student will learn in this unit is the standard form ( MACROBUTTON MTEditEquationSection2 Equation Section (Next) SEQ MTEqn \r \h \* MERGEFORMAT  SEQ MTSec \h \* MERGEFORMAT ), and the vertex form ().  In both these equations the “a” value is what determines the vertical change.  If a > 0, then the parabola opens up and the function has a minimum value.  If a < 0, the parabola opens down and the function has a maximum value.  In the vertex form, the “p” and “q” values can be used to determine the vertex of the parabola.  In this section, the student will also learn how to switch from the standard form to the vertex form and vice versa.

Study Tips,  Methods  and or Advice

Example 1

Write the equation  in the form.   

Step 1: Expand.                             

Step 2: Remove Brackets.              

Step 3: Collect like terms.              

Example 2

Write the equation  in the form.   

Step 1: Expand.                             

Step 2: Remove Brackets.             

Step 3: Collect like terms.              

When switching from standard form to vertex form, it can sometimes be difficult.  This method will help you switch between the standard and vertex form with ease.  This method is referred to as completing the square.

Example 3

Write the equation in the form.

Step 1: Remove -1 as a                  

common factor for the

first two terms.

Step 2: Within the brackets,           

add and subtract the square

of (-6); that is  = 9

Step 3: Write the first three          

terms in the brackets as a                 

perfect square.  Multiply the             

fourth term in the brackets

by -1.

Tips: For step 3 when you are writing the first three terms in the brackets as a perfect square, all you have to do is divide the middle term by 2.  In the example above,, take the second term(-6) and divide it by two.

Sample Questions and complete solutions

Extra Practice Questions and Answers

Self Reflection

Personal Reflection – Azan

     My name is Azan Peermohamed and my topic is the standard and vertex forms for quadratic functions.  This topic is fairly simple and I didn’t encounter that many problems while completing this project.   In my opinion I think that the most challenging part of this topic is completing the square when switching from standard to vertex form.   After some practice of switching from standard to vertex form, it should be easy.  Students taking Functions and Relations should find this unit to be easy and fun.