Lösung 2.3:6a - Versionsgeschichte

Tek: Added caption

2009-08-19T12:41:27Z

Added caption

← Nächstältere Version		Version vom 12:41, 19. Aug. 2009
Zeile 10:		Zeile 10:


-	<center>{{:2.3.6a - Solution - The parabola y = (x - 1)²}}</~~center~~>	+	{\| align="center"
		+	\|align="center"\|{{:2.3.6a - Solution - The parabola y = (x - 1)²}}
		+	\|-
		+	\|align="center"\|<small>Der Graph von ''f''(''x'') = (''x'' - 1)²</small>
		+	\|}

2009-08-19T12:35:40Z

Replaced figure with metapost figure

← Nächstältere Version		Version vom 12:35, 19. Aug. 2009
Zeile 10:		Zeile 10:


-	~~[[Image~~:~~2_3_6_a~~.~~gif\|~~center]]	+	<center>{{:2.3.6a - Solution - The parabola y = (x - 1)²}}</center>

2009-06-09T13:55:25Z

← Nächstältere Version		Version vom 13:55, 9. Jun. 2009
Zeile 1:		Zeile 1:
-	Mit der binomischen Formel <math>(a+b)^2=a^2+2ab+b^2</math>, sehen wir dass der ~~quadratischer Ausdruch~~ <math>(x-1)^{2}\,</math> ist	+	Mit der binomischen Formel <math>(a+b)^2=a^2+2ab+b^2</math> sehen wir, dass der quadratische Ausdruck <math>(x-1)^{2}\,</math> ist

	{{Abgesetzte Formel\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}
Zeile 7:		Zeile 7:


-	Hinweis: Zeichnen wir die ~~Graphe~~ von <math>y=(x-1)^{2}</math>, sehen wir dass die Funktion ein Minimum in <math>x=1\,</math> hat.	+	Hinweis: Zeichnen wir die Graph von <math>y=(x-1)^{2}</math>, sehen wir dass die Funktion ein Minimum in <math>x=1\,</math> hat.


	[[Image:2_3_6_a.gif\|center]]		[[Image:2_3_6_a.gif\|center]]

2009-03-16T17:06:11Z

← Nächstältere Version		Version vom 17:06, 16. Mär. 2009
Zeile 1:		Zeile 1:
-	~~Using the rule~~ <math>(a+b)^2=a^2+2ab+b^2</math>, ~~we recognize the polynomial as the expansion of~~ <math>(x-1)^{2}\,</math>,	+	Mit der binomischen Formel <math>(a+b)^2=a^2+2ab+b^2</math>, sehen wir dass der quadratischer Ausdruch <math>(x-1)^{2}\,</math> ist

	{{Abgesetzte Formel\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}

-	~~This quadratic expression has its smallest value~~, ~~zero~~, ~~when~~ <math>x-1=0</math>, ~~i.e.~~	+	Die Funktion nimmt ihren kleinsten Wert, null an, wenn <math>x-1=0</math>, also wenn
-	<math>x=1</math>. ~~All non-zero values of~~ <math>x-1</math> ~~give a positive value for~~	+	<math>x=1</math>. Alle anderen Werten von <math>x-1</math> ergeben einen positiven Ausdruck <math>(x-1)^{2}</math>.
-	<math>(x-1)^{2}</math>.	+


-	~~Note~~: ~~If we draw the curve~~ <math>y=(x-1)^{2}</math>, ~~we see that it has a minimum value of zero at~~ <math>x=1\,</math>.	+	Hinweis: Zeichnen wir die Graphe von <math>y=(x-1)^{2}</math>, sehen wir dass die Funktion ein Minimum in <math>x=1\,</math> hat.


	[[Image:2_3_6_a.gif\|center]]		[[Image:2_3_6_a.gif\|center]]

2008-10-22T14:12:25Z

hat „Solution 2.3:6a“ nach „Lösung 2.3:6a“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 14:12, 22. Okt. 2008

2008-10-22T08:33:58Z

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 08:33, 22. Okt. 2008
Zeile 1:		Zeile 1:
	Using the rule <math>(a+b)^2=a^2+2ab+b^2</math>, we recognize the polynomial as the expansion of <math>(x-1)^{2}\,</math>,		Using the rule <math>(a+b)^2=a^2+2ab+b^2</math>, we recognize the polynomial as the expansion of <math>(x-1)^{2}\,</math>,

-	{{~~Displayed math~~\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}

	This quadratic expression has its smallest value, zero, when <math>x-1=0</math>, i.e.		This quadratic expression has its smallest value, zero, when <math>x-1=0</math>, i.e.

2008-09-29T11:29:19Z

← Nächstältere Version		Version vom 11:29, 29. Sep. 2008
Zeile 1:		Zeile 1:
-	Using the ~~squaring~~ rule, we recognize the polynomial as the expansion of	+	Using the rule <math>(a+b)^2=a^2+2ab+b^2</math>, we recognize the polynomial as the expansion of <math>(x-1)^{2}\,</math>,
-	<math>~~\left~~( x-1 ~~\right~~)^{2}</math>,	+

		+	{{Displayed math\|\|<math>x^{2}-2x+1 = (x-1)^{2}\,\textrm{.}</math>}}

-	<math>x~~^{2}~~-~~2x+~~1=~~\left~~( x-1 ~~\right~~)^{2}</math>	+	This quadratic expression has its smallest value, zero, when <math>x-1=0</math>, i.e.
		+	<math>x=1</math>. All non-zero values of <math>x-1</math> give a positive value for
		+	<math>(x-1)^{2}</math>.


-	~~This quadratic expression has its smallest value, zero, when~~	+	Note: If we draw the curve <math>y=(x-1)^{2}</math>, we see that it has a minimum value of zero at <math>x=1\,</math>.
-	~~<math>x-\text{1}=0</math>, i.e.~~	+
-	~~<math>x=\text{1}</math>. All non-zero values of~~	+
-	~~<math>x-\text{1}</math>~~	+
-	~~give a positive value for~~	+
-	~~<math>\left( x-1 \right)^{2}</math>.~~	+
-		+
-	~~NOTE~~: If we draw the curve	+
-	<math>y=~~\left~~( x-1 ~~\right~~)^{2}</math>, we see that it has a minimum value of zero at	+
-	<math>x=\~~text{1}~~</math>.	+


	[[Image:2_3_6_a.gif\|center]]		[[Image:2_3_6_a.gif\|center]]

2008-09-21T10:51:26Z

← Nächstältere Version		Version vom 10:51, 21. Sep. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	Using the squaring rule, we recognize the polynomial as the expansion of
-	<~~center~~> ~~[[Image:2_3_6a~~.~~gif]]~~ </~~center~~>	+	<math>\left( x-1 \right)^{2}</math>,
-	{{~~NAVCONTENT_STOP~~}}	+
		+
		+	<math>x^{2}-2x+1=\left( x-1 \right)^{2}</math>
		+
		+
		+	This quadratic expression has its smallest value, zero, when
		+	<math>x-\text{1}=0</math>, i.e.
		+	<math>x=\text{1}</math>. All non-zero values of
		+	<math>x-\text{1}</math>
		+	give a positive value for
		+	<math>\left( x-1 \right)^{2}</math>.
		+
		+	NOTE: If we draw the curve
		+	<math>y=\left( x-1 \right)^{2}</math>, we see that it has a minimum value of zero at
		+	<math>x=\text{1}</math>.
		+
		+
	[[Image:2_3_6_a.gif\|center]]		[[Image:2_3_6_a.gif\|center]]

2008-09-09T09:02:03Z

← Nächstältere Version

Version vom 09:02, 9. Sep. 2008

2008-08-21T06:48:09Z

Robot: Automated text replacement (-[[Bild: +[[Image:)