3Tvwo § 7.3 Rearranging quadratic formulas

§ 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.

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§ 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.

Slide 1 - Diapositive

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 § !

Slide 2 - Diapositive

From a formula like:
f(x) = ax^2 + bx + c ,
you can find the
A
vertex of the graph
B
p.o.i. with the y-axis
C
p.o.i. with the x-axis
D
most important things in life

Slide 3 - Quiz

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)

Slide 4 - Diapositive

From a formula like:
g(x) = a(x – s) (x – t)
you can find the
A
vertex of the graph
B
most beautiful things on earth
C
p.o.i. with the y-axis
D
p.o.i. with the x-axis

Slide 5 - Quiz

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)

Slide 6 - Diapositive

From a formula like:
k(x) = a(x-p)^2 + q
You can find the
A
secret you were looking for all your life
B
p.o.i. with y-axis
C
p.o.i. with x-axis
D
vertex

Slide 7 - Quiz

An example of the previous question:
k(x) = 4(x-6)^2 + 9
The vertex for the graph is:
(6 , 9)

Slide 8 - Diapositive

COMPLETING THE SQUARE 
is important in this chapter!
First of all: try to find in the book, on which pages this was treated!

Slide 9 - Diapositive

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

Slide 10 - Carte mentale

And the good answer is:
§ 4.2 on page 122 and further!

Slide 11 - Diapositive

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) 

Slide 12 - Diapositive

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!

 

Slide 13 - Diapositive

Slide 14 - Diapositive

 HOMEWORK Time!

Slide 15 - Diapositive

What did you learn this lesson?

Slide 16 - Carte mentale

Slide 17 - Diapositive

Slide 18 - Diapositive