Reading

For this topic, you will need to read and work through pages 217-221 in your textbook.

In the last module you learned to factorise quadratics of the form $ax^2+bx+c$

You also learned that not all equations have solutions that are whole numbers.

For example:

$x^2+3x+2=0$ does have integral solutions $(x= +1, +2)$ ;

but $x^2+3x+1=0$ does not.

Now you will learn two methods to find these solutions.

(The answers to the second equation are -0.38 and -2.61).

You need to be very careful with negative signs when using these methods and give your answers to 2 d.p. (don't leave the square root signs in). All your answers can be checked by substitution.

Make sure you cover the following:

Solving quadratic equations by the quadratic formula (Extended)
Solving quadratic equations by completing the square (Extended)

Make sure you do all of Exercises 13G and 13H.

Tutorial

Watch the MathsWatch tutorials using the links below:

At the top of each MathsWatch tutorial screen there are tabs for Interactive Questions and a downloadable Worksheet, which we recommend that you use to practice what you’ve learnt. Answers for these worksheets are found in General Resources as well as a reminder of how to login to MathsWatch.

WATCH - Solving Quadratics with the Formula (MathsWatch)

WATCH - Completing the Square Basics (MathsWatch)

WATCH - Completing the Square Solving (MathsWatch)

Practice

Now work through the MyMaths activities:

EXPLORE - Quadratic Formula (MyMaths)

EXPLORE - Completing the Square (MyMaths)

Download

WORKSHEET - Solving Equations by Completing the Square (Kuta Software)

Link Icon.png Links

WATCH - Solving equations involving area and perimeter (YouTube)

EXPLORE - an algebraic rectangle (SSDD Problems)

EXPLORE - the power of 0 (SSDD Problems)

EXPLORE - A rectangle and 2 algebraic fractions (SSDD Problems)