3Tvwo Ch 7 REFRESH

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Ch 7 Quadratic functions

First:  REFRESH !

Before you work on your own...

let's do a few things together!

Open your book 3A, p.234/235

R1 a,b,c

Your teacher will show you how to work out:

SIMULTANEOUS EQUATIONS,

by working out R1 a,b,c.

Now write down in your Notebook:

'Ch 7 Quadratic equations.'

and solve:

R2 h:                  (2x + 5)squared - 5 = 31

 

The answer to
R2h (2x + 5)squared - 5 = 31 is

1. x = - 1/2 and x = 5.5
2. x = 1/2 and - 5 1/2
3. x = 1/2 and x = 5.5
4. x = 0.5 and x = - 5.5

Solution to R2h:

(2x + 5) squared - 5 = 31

(2x + 5) squared = 36

2x + 5 = 6  or  2x + 5 = -6

2x = 1  or  2x = -11

x = 1/2  or  x = -5.5

Write down in your Notebook:

'R3 f:                        y = x squared + 4x - 10'

and write this in the form:

y = (x + p) squared + q

(so do: completing the square!

If needed: Study 'Theory' above R3!)

When you rewrite R3f:
y = x squared + 4x - 10,
completing the square, you get:

1. y = (x + 4) squared - 10
2. y = (x + 2) squared - 6
3. y = (x - 2) squared - 14
4. y = (x + 2) squared - 14

Solution to R3f:

y = x squared + 4x - 10

y = (x + 2) squared -4 -10

y = (x + 2) squared - 14

Now a Math joke!

One more task for you!

Write down:

R4f                      14x squared + x - 3 = 0

and solve this one with the quadratic formula.

(Forgotten how it works? Next to R4 there is an explanation!)

The answer to
R3f 14x squared + x -3 =0 is

1. x = 3/7 or -0.5
2. x = -0.429 or x = -0.5
3. x = 0.429 or x = -0.5
4. x = 2 1/3 or x = - 1/2

 Solution to R4f:

14x squared + x -3 = 0

D = b squared -4ac = 1 squared -4 times 14 times -3 = 

1 + 168 = 169

x = (-1 + root 169) : 28    or   x = (-1 - root 169) : 28 

x = (-1 + 13) : 28    or   x = (-1 - 13) : 28

x = 12/28   or   x = (-14) : 28

x = 3/7   or   x = - 1/2

Time to do Homework!

Homework = Refresh Ch 7, p.234/235

ATTENTION:

From exercises R2, 3 and 4,  choose half of them.

For example, from R2 you do a, b, c,d

from R3 you do c, d ,e,  etc.