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9 mei - 3H §3.4 / 3V §3.5: f(x)=a(x-d)(x-e)
Mail in de vakantie - vragen?
toets inplannen?
uitleg nodig van opdracht?
3 Havo en Vwo
1 / 38
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Slide 1:
Slide
Wiskunde
Middelbare school
havo, vwo
Leerjaar 3
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Lesson duration is:
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Mail in de vakantie - vragen?
toets inplannen?
uitleg nodig van opdracht?
3 Havo en Vwo
Slide 1 - Slide
Terugblik - vragen?
Havo §3.1 - §3.3
Vwo §3.1 en §3.3 (§3.2 volgend uur)
Slide 2 - Slide
ontbinden in factoren / herleiden
vergelijking oplossen
Verschil !!
x
2
+
3
x
+
2
x
2
+
3
x
+
2
=
0
Slide 3 - Slide
ontbinden in factoren / herleiden
vergelijking oplossen
Verschil !!
3
(
x
2
+
3
x
+
2
)
=
x
2
+
3
x
+
2
=
0
3
(
x
+
1
)
(
x
+
2
)
(
x
+
1
)
(
x
+
2
)
=
0
(
x
+
1
)
=
0
(
x
+
2
)
=
0
V
x
=
−
1
V
x
=
−
2
3
x
2
+
9
x
+
6
=
0
3
x
2
+
9
x
+
6
=
Slide 4 - Slide
a
x
2
+
b
x
+
c
=
0
a
x
2
+
b
x
=
0
a
x
2
=
c
Ontbinden in factoren
(
x
+
1
)
(
x
+
2
)
=
0
x
+
1
=
0
x
+
2
=
0
V
V
x
=
−
1
x
=
−
2
x
2
+
3
x
+
2
=
0
x
2
+
3
x
=
0
x
(
x
+
3
)
=
0
x
=
0
V
x
+
3
=
0
x
=
0
V
x
=
−
3
x
2
=
3
x
=
√
3
V
x
=
−
√
3
Slide 5 - Slide
Verschil !!
x
2
+
3
x
+
2
=
1
2
x
2
+
3
x
+
2
=
0
Slide 6 - Slide
Verschil !!
x
2
+
3
x
+
2
=
1
2
x
2
+
3
x
+
2
=
0
(
x
+
1
)
=
0
(
x
+
1
)
(
x
+
2
)
=
0
(
x
−
2
)
=
0
(
x
+
5
)
=
0
V
x
=
2
V
x
=
−
5
(
x
−
2
)
(
x
+
5
)
=
0
x
2
+
3
x
−
1
0
=
0
V
(
x
+
2
)
=
0
x
=
−
1
V
x
=
−
2
Slide 7 - Slide
Verschil !!
x
2
+
3
x
+
2
=
1
2
x
2
+
3
x
+
2
=
0
Dus: ... ??
(
x
+
1
)
(
x
+
2
)
=
1
2
Slide 8 - Slide
Hoe gebruik je dit?
kwadratische formules
Slide 9 - Slide
Hoe gebruik je dit?
§6.1 - §6.3
3 Havo
Havo §3.2 opgave 17
h
=
−
2
,
5
x
2
+
6
x
Slide 10 - Slide
Hoe gebruik je dit?
§6.1 - §6.3
3 Havo
(Vwo gemengde opgaven H3, opgave 7)
h
=
−
0
,
2
(
x
−
3
,
2
)
2
+
4
,
0
4
8
Slide 11 - Slide
Havo §3.4
Vwo §3.5 Theorie A (Theorie B in volgende les)
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
Slide 12 - Slide
Verschil Overeenkomst!!
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
Slide 13 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
b
=
c
=
d
=
e
=
Slide 14 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
b
=
c
=
d
=
e
=
Slide 15 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
2
b
=
c
=
d
=
e
=
Slide 16 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
2
b
=
1
4
c
=
d
=
e
=
Slide 17 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
2
b
=
1
4
c
=
−
1
6
d
=
e
=
Slide 18 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
2
b
=
1
4
c
=
−
1
6
d
=
−
8
e
=
Slide 19 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
a
=
2
b
=
1
4
c
=
−
1
6
d
=
−
8
e
=
1
Slide 20 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
Slide 21 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
2
x
2
+
1
4
x
−
1
6
=
0
Slide 22 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
2
x
2
+
1
4
x
−
1
6
=
0
2
(
x
+
8
)
(
x
−
1
)
=
0
(
x
+
8
)
=
0
(
x
−
1
)
=
0
V
x
=
−
8
V
x
=
1
Slide 23 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
x
=
−
8
V
x
=
1
dus: ??
Slide 24 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
x
=
−
8
V
x
=
1
dus:
en
(
−
8
,
0
)
(
1
,
0
)
Slide 25 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
x
=
−
8
V
x
=
1
dus:
en
(
−
8
,
0
)
(
1
,
0
)
snijpunten met x-as:
x
=
d
en
x
=
e
dus: ??
Slide 26 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
2
x
2
+
1
4
x
−
1
6
f
(
x
)
=
2
(
x
+
8
)
(
x
−
1
)
Verschil Overeenkomst!!
snijpunten met x-as:
x
=
−
8
V
x
=
1
dus:
en
(
−
8
,
0
)
(
1
,
0
)
snijpunten met x-as:
x
=
d
en
x
=
e
dus:
(
−
8
,
0
)
en
(
1
,
0
)
Slide 27 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
Top
Slide 28 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
Top
Slide 29 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
Slide 30 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
Slide 31 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
2
2
−
4
⋅
2
−
5
=
−
9
Slide 32 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
2
2
−
4
⋅
2
−
5
=
−
9
dus:
Slide 33 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
2
2
−
4
⋅
2
−
5
=
−
9
dus: top is
(
2
,
−
9
)
Slide 34 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
2
2
−
4
⋅
2
−
5
=
−
9
dus: top is
(
2
,
−
9
)
Symmetrie, dus top is:
x
top
=
2
(
d
+
e
)
Slide 35 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
2
2
−
4
⋅
2
−
5
=
−
9
dus: top is
(
2
,
−
9
)
Symmetrie, dus top is:
x
top
=
2
(
d
+
e
)
=
2
(
−
1
+
5
)
=
2
Slide 36 - Slide
f
(
x
)
=
a
(
x
−
d
)
(
x
−
e
)
f
(
x
)
=
a
x
2
+
b
x
+
c
f
(
x
)
=
x
2
−
4
x
−
5
f
(
x
)
=
(
x
+
1
)
(
x
−
5
)
Verschil Overeenkomst!!
x
top
=
−
2
a
b
=
−
2
⋅
1
−
4
=
2
Top
y
top
=
2
2
−
4
⋅
2
−
5
=
−
9
dus: top is
(
2
,
−
9
)
Symmetrie, dus top is:
x
top
=
2
(
d
+
e
)
=
2
(
−
1
+
5
)
=
2
y
top
=
(
2
+
1
)
(
2
−
5
)
=
−
9
dus: top is
(
2
,
−
9
)
Slide 37 - Slide
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Slide 38 - Slide
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