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1TH/vwo §11.5 Quadratic formulas
§11.5 Quadratic formulas
+ §12.4 Linear formulas was about STRAIGHT LINES.
+ §12.5 Quadratic formulas is about PARABOLAS.
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Wiskunde
Middelbare school
havo, vwo
Leerjaar 1
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24 slides
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interactive quizzes
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text slides
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Lesson duration is:
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§11.5 Quadratic formulas
+ §12.4 Linear formulas was about STRAIGHT LINES.
+ §12.5 Quadratic formulas is about PARABOLAS.
Slide 1 - Slide
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.
Slide 2 - Slide
Slide 3 - Slide
Remember your answer and key it in in the next slide.
timer
0:20
Slide 4 - Slide
Quadratic formulas are:
A
abcd
B
abc
C
abd
D
c
Slide 5 - Quiz
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!
Slide 6 - Slide
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
Slide 7 - Slide
graph for: =
This is the 'Mother' of all
Quadratic Graphs!
y
x
2
Slide 8 - Slide
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
Slide 9 - Slide
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
Slide 10 - Slide
Slide 11 - Slide
Task:
What is the main difference
between this graph and the one
for ?
Teacher gives a few turns to several pupils.
y
=
x
2
Slide 12 - Slide
Slide 13 - Slide
Now follow a few tasks to ...
give you the neccessary practice for doing the
Homework.
Slide 14 - Slide
Calculate when x = -6
y
=
x
2
timer
0:20
A
-36
B
12
C
-12
D
36
Slide 15 - Quiz
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
Slide 16 - Slide
TASK:
Now when x = -4,
calculate
Remember and key in, in the next slide!
y
=
x
2
−
3
y
Slide 17 - Slide
Calculate , when
y
=
x
2
−
3
x
=
−
4
timer
0:30
A
-13
B
-7
C
-11
D
13
Slide 18 - Quiz
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
Slide 19 - Slide
Homework time - later a little more information
about §12.5 follows in this Lesson Up.
Do: §12.5 Quadratic formulas
Havo and H/V, Do: S37, 37, 38, S39 and 39
VWO, Do: 38, 39, 40, C9 and C10
NOTE: Study the Theory parts when they come up!
Slide 20 - Slide
Finally ...
You'll learn how to CHECK if a certain point lies on a graph.
We will study the Method HOW to check this.
If this isn't clear to you, then
study the Method on p.188, when doing the Homework.
Slide 21 - Slide
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?
Let's study the Theory in the next slide together.
Slide 22 - Slide
Slide 23 - Slide
Homework time
Do: §11.5 Quadratic formulas
Havo and H/V, Do: S37, 37, 38, S39 and 39
VWO, Do: 38, 39, 40, C9 and C10
NOTE: Study the Theory parts when they come up!
Slide 24 - Slide
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