1TH/vwo §11.5 Quadratic formulas

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

§11.5 Quadratic formulas

+  §12.4 Linear formulas was about  STRAIGHT LINES. 

+ §12.5 Quadratic formulas is about  PARABOLAS (?!)

    When following this LessonUp you will learn what

    this is. 

Graphs, graphs, graphs ...

As some graphs will be drawn by you in this paragraph,

now take before you:

+ your Notebook 

+ a pencil, eraser and geo 

In other words: The Right Stuff.     

Remember your answer and key it in in the next slide.

Quadratic formulas are:

1. abcd
2. abc
3. abd
4. c

Solution:

As you've just learned, in order to be a Quadratic Formula,

there must be a SQUARE of a VARIABLE in it!

So this rings true for: a, b and d.

Formula c contains a square all right, but not the square of a variable!

Have you got a clue...

what the GRAPH for the FORMULA             = 

looks like?

Next 2 slides show you all about it.

And more! 

x​2​​

y

graph for:          =

This is the 'Mother' of all

Quadratic Graphs!

y

x​2​​

Some points of attention for 

the graph of:            =

+ watch the nicely rounded shape

+ it's name is: a PARABOLA

+ some 'easy to find' points in the 

    table are: (3, 9), (1, 1) but also:

    (-3,9) and (-1,1)

y

x​2​​

Some points of attention for 

the graph of:            =

ATTENTION: The y coordinate is higher than the

x coordinate most of the times. Just look at the Table.

QUESTION:  Mention an EXCEPTION to this rule in the next slide!

Watch the Graph closely once more.

y

x​2​​

Some points of attention for 

the graph of:            =

ATTENTION: The y coordinate is higher than the

x coordinate most of the times. Just look at the Table.

QUESTION:  Mention an EXCEPTION to this rule in the next slide!

Watch the Graph closely once more.

y

x​2​​

 This GRAPH for the formula:

y =            is ....

the BASIC QUADRATIC GRAPH!

In this paragraph you will

meet more quadratic graphs, that

are all variations of this one.

Next slide shows you a graph that is derived from (=afgeleid van) the

Basic graph.

x​2​​

Task:

What is the main difference 

between this graph and the one

for                                           ?

Teacher gives a turn to several pupils.

y=x​2​​

Now follow a few tasks to ...

give you the neccessary practice for doing the

Homework.

Calculate
when x = -6

y=x​2​​

1. -36
2. 12
3. -12
4. 36

Solution:

y = 

when we fill in:  x = -6,  we need BRACKETS:

y =             = -6 x -6 = 36   (and not -36!)

Let's practice a bit more with this, as it will make doing

your homework easier!

x​2​​

(−6)​2​​

TASK:       

Now when x = -4,

calculate 

Remember and key in, in the next slide!

y=x​2​​−3

y

Calculate
, when

y=x​2​​−3

x=−4

1. -13
2. -7
3. -11
4. 13

SOLUTION:               y =      -3

Now when x = -4,  we replace the variable      by  -4, as follows:

y =            - 3  =            -3  =  -4  x  -4  -3 = 16 - 3 = 13

x​2​​

x

x​2​​

(−4)​2​​

Homework time - later some more information

about §12.5 follows in this Lesson Up.

Do:    §12.5 Quadratic formulas  

Havo and H/V,  Do: 33, S35, 36, 37, 38, S39

VWO,                     Do: 

NOTE:     Study the Theory parts when they come up!

Finally ...

You'll learn how to CHECK if a certain point lies on a graph.

We will study the Method HOW to check this later this lesson.

For this we will use the Method on p.188.

Homework time

Do:    §11.5 Quadratic formulas                                      

Havo and H/V,  Do: S35, 36, 37, 38 and S39 

VWO,                     Do: 37, 38, 39, 40, C9 and C10

NOTE:     Study the Theory parts when they come up!

Suppose you have a graph and a point ...

and you want to know IF that point lies on the graph.

What to do to know for sure?

This is not about READING OFF from a graph, but about CALCULATING!

Let's study the Theory in the next slide together.

Homework time

Do:    §11.5 Quadratic formulas  

H/V : 

Do: SUPPORT PATH:  So do all tasks, but instead of

        35 do S35  and instead of 39 do S39!