Summary
Wiskunde samenvatting hoofdstuk 4 Werken met formules
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Dit is een korte samenvatting van de meest belangrijke dingen uit hoofdstuk 4 werken met formules.
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Wiskunde samenvatting hf 4Voorkennis:
- 4 omhoog → y = 2x2 + 4 (y-as)
- 4 omlaag → y = 2x2 - 4 (y-as)
- 4 rechts → y = 2 (x - 4)2 (x-as)
- 4 links → y = 2 (x + 4) (x-as)
Top parabool: y = a (x - p)2 + q
(p,q) = top
a > 0 dalparabool
a < 0 bergparabool
Paragraaf 4.1:
Parabool: y = a (x - d)(x - e)
Snijpunt x-as → y = 0
0 = a (x - d)(x - e)
x-d=0vx-e=0
x=dvx=e
d +e
Xtop =
2
Ytop = x top invullen op de plaats van de x
y = a (x - p)2 + q
Parabool met top (4,5) door (1,23)
y = a (x - 4)2 + 5
Door (1,23)
a (1 - 4)2 + 5 = 23
a (-3)2 + 5 = 23
9a + 5 = 23
9a = 18
a=2
y = 2 (x - 4)2 + 5
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
y = ax2 + bx + c
−b
Xtop =
2a
Ytop = X top invullen op de plaats van de X
Paragraaf 4.2:
1. X even → wortel positief ⇒ 2 oplossingen
2. X even → wortel negatief ⇒ geen oplossing
3. X oneven → wortel positief ⇒ 1 oplossing
4. X oneven → wortel negatief ⇒ 1 oplossing
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