# 2Tvwo §5.4 Quadratic formulas 2!

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Slide 1: Tekstslide
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

In deze les zitten 21 slides, met tekstslides. Lesduur is: 50 min

## Onderdelen in deze les

#### Slide 1 -Tekstslide

Removing brackets
§5.4 and §5.5 do NOT require you to remove brackets and write formulas shorter.
No, these paragraphs are about GRAPHS !
What have they got to do with §5.1 / §5.2 and §5.3 ?!
Well, the quadratic formulas from those paragraphs
can be used for making the graphs from §5.4 and §5.5.

#### Slide 2 -Tekstslide

is a quadratic formula (it has a variable squared)

If we want to plot the graph of this formula, we should first make a table. Take the horizontal axis from -3 to 7.
y=2x28x

#### Slide 3 -Tekstslide

Filling in a NEGATIVE number in a quadratic formula:

#### Slide 4 -Tekstslide

Plotting the graph for a quadratic formula .....
requires a TABLE with x- and y-values, that we can FILL IN in a
COORDINATE SYSTEM.
Below you see the result. (By the way, we could do with less points.)
In case you think: how on earth do we get the y-outcomes for these
x values, then watch the next slide!

#### Slide 5 -Tekstslide

Filling in numbers in a quadratic formula:

By the way:
+  we will discuss a few of these
calculations
+  normally we do these kinda
+ write the results in the table!

#### Slide 6 -Tekstslide

Plotting the graph for a quadratic formula

This table shows us we should take:
- the horizontal axis from -3 to 7 (with steps of 1)
- the vertical axis from - 10 to 45 (with steps of 5)

#### Slide 7 -Tekstslide

Plotting the graph for a quadratic formula
Here

#### Slide 8 -Tekstslide

Plotting the graph for a quadratic formula

Plot all points from the table

#### Slide 9 -Tekstslide

Plotting the graph for a quadratic formula

Finally:
Connect them with a smooth   line.                                       line curve             l                We call this a PARABOLA.
Now a chess Joke!

#### Slide 11 -Tekstslide

Upward or downward opening parabola
In the coordinate system on the
right, the green graphs are
upward opening parabolas
and the purple graphs are
downward opening parabolas.

#### Slide 12 -Tekstslide

Upward or downward opening parabola
Graphs for a quadratic formula are
called parabolas
This parabola is an
upward opening parabola.

Notice that the number 2, before
the          ,  is POSITIVE.
y=2x28x
x2

#### Slide 13 -Tekstslide

Upward or downward opening parabola
You will find that you can tell from the formula if a parabola is upward or downward opening.

If the number in front of
is positive, it is upward opening
If the number in front of
is negative, it is downward opening.
x2
x2

#### Slide 14 -Tekstslide

Vertex
The lowest point in an
upward opening parabola,
or the highest point in a
downward opening parabola
is called the vertex.

#### Slide 15 -Tekstslide

Axis of symmetry
All parabolas have
reflection symmetry.
The vertical line through
the vertex is the axis of symmetry
All vertical lines have a formula
x = ....

One more chess joke follows.

#### Slide 20 -Tekstslide

HOMEWORK

Make and correct §5.4
You may SKIP:    24 and 25
Then take pics and send in the lot in GC.