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1TTO §12.5 Quadratic formulas
§12.5 Quadratic formulas
Ultra short recap and a look forward too:
+ §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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interactive quizzes
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Lesson duration is:
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§12.5 Quadratic formulas
Ultra short recap and a look forward too:
+ §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:
+ Notebook
+ Pencil, eraser and geo
Slide 2 - Slide
Slide 3 - Slide
Remember your answer and key it in in the next slide.
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: =
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
So this graph for the formula:
y = is ....
the BASIC QUADRATIC GRAPH!
In this paragraph you will
meet more quadratic graphs, that
are all variations to 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
Calculate y = x squared when x = -6
A
-36
B
12
C
-12
D
36
Slide 12 - 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 13 - Slide
TASK: y = - 3
Now when x = -4,
what is y ?
Remember and key in in the next slide!
x
2
Slide 14 - Slide
A
-13
B
5
C
-11
D
13
Slide 15 - 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 16 - 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, don't worry.
It's all in §12.5 and you can study the Method as long as you need!
Slide 17 - 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 18 - Slide
Slide 19 - Slide
Homework time
Remember to Study the Theory parts (again) when they come up!
Slide 20 - Slide
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