3Tvwo § 4.4 Choose the best Method! (1)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

§ 4.4 Quadratic equations

Which method is the best for a specific exercise?

That's what we are going to find out now!

Mention one Method for solving a Quadratic Equation.

SUMMARISING:

There are (at least) 5 Methods, that you learnt. In the next slide they come up.

The 5 Methods

1.    using:   A x B = 0, then A=0 or B=0

2.   by:    Cards                                                       

3.   by:   Factorising   

4.   by:   Completing the square

5.   by:   the Quadratic Formula

Choose the best Method for:
Solve 8(x - 7)(2x + 5) = 0

1. Cards
2. A x B = 0
3. Factorising
4. Completing the square

Once more 8(x-7)(2x + 5) = 0

A common mistake here is:

+  working out the brackets

+ making a few calculating mistake along the way

+ getting the wrong answer(s)

How to do it you see on the next slide!

Solve 8(x - 7)(2x + 5) = 0

Only 2 steps I will show here:

divide by 8 on both sides of the = sign  :

(x -7)(2x + 5) = 0

Now use the scheme  A x B = 0,  so work out:

x - 7 = 0   or  2x + 5 = 0, etcetera!

The same for:
Solve (x - 6)squared = 16

1. Completing the square
2. Quadratic Formula
3. Cards
4. A x B = 0

The same for:
Solve 3 a squared + 24a = 0

1. Quadratic Formula
2. A x B = 0
3. Completing the square
4. Factorising

The same for:
b squared + 6b + 5 = 13

1. A x B = 0
2. Factorising
3. Quadratic Formula
4. Completing the square

Once more b squared + 6b = 13

You can only see well how to solve it, after you have simplified the equation as follows:                       b squared + 6b - 13 = 0

Now you can see that there are no two numbers that are:

+  multiplied equal to -13  and

+ added up equal to + 6 

So this leads us to:  C Quadratic Formula, or also D Completing the square!

The same with:
3 c squared - 5c + 2 = 0

1. Quadratic Formula
2. Factorising
3. A x B = 0
4. Cards

By the way .....

We just dealt with 5 Quadratic Equations, 

taken from:

Theory, p.131             

If you want to know how to work them out, 

Study this page!

Do § 4.4 = Homework

A few notes on the content:

- in exercises 26, 27 and 28 you are 'taken by the hand' ;

so the Best Method is chose for you

- in 29 and 30 however, you will have to find the Best Method yourself!

Work in silence for 10 minutes.