3Tvwo § 7.3 Rearranging quadratic formulas

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

§ 7.3 Rearranging quadratic formulas

What this means and what it is for, you'll learn in this lesson.

That is, if you pay attention.

Some questions...

Try to answer the following questions as good as you can.

It is not important to have them all correct.

Just by thinking about it, you will learn what is needed in this § !

From a formula like:
f(x) = ax^2 + bx + c ,
you can find the

1. vertex of the graph
2. p.o.i. with the y-axis
3. p.o.i. with the x-axis
4. most important things in life

An example of the previous question:

f(x) = 3x² + 4x - 6

The p.o.i. with the y-axis you find by filling in x = 0.

Then you'll find that f(0) = 0 + 0 - 6 = -6

So the answer is (0 , -6)

From a formula like:
g(x) = a(x – s) (x – t)
you can find the

1. vertex of the graph
2. most beautiful things on earth
3. p.o.i. with the y-axis
4. p.o.i. with the x-axis

An example of the previous question:

h(x) = -5(x – 6)(x + 2)

Make this expression equal to 0 :

-5(x - 6)(x + 2) = 0,   so   (x - 6) = 0   or   (x + 2) = 0

The p.o.i. with the x-axis are:

(6 , 0)  and  (-2 , 0)

From a formula like:
k(x) = a(x-p)^2 + q
You can find the

1. secret you were looking for all your life
2. p.o.i. with y-axis
3. p.o.i. with x-axis
4. vertex

An example of the previous question:

k(x) = 4(x-6)^2 + 9

The vertex for the graph is:

(6 , 9)

COMPLETING THE SQUARE 

is important in this chapter!

First of all: try to find in the book, on which pages this was treated!

Completing the square is treated in paragraph: ...........

And the good answer is:

§ 4.2 on page 122 and further!

This is how completing the square works:

1.    f(x) = x² + 6x – 5                                   Take half of 6 and then:

2.     f(x) = (x+3)² – 9 - 5                              This -9 is because (x + 3)² includes +9,

                                                                               which is not in line 1. 

3.     f(x) = (x+3)²  – 14

From this expression you can now  read off the vertex:         (- 3, -14) 

Theory p.245 § 7.3

In the Theory on the next slide there is happening so much (!) that I think it wise to go through it together, now!

Maybe you do not agree with me, that it is 'complicated'.

All the better!

 

 HOMEWORK Time!

What did you learn this lesson?