Lösung 2.3:8c - Versionsgeschichte

Silke um 16:37, 23. Aug. 2009

Silke — Sun, 23 Aug 2009 16:37:32 GMT

← Nächstältere Version		Version vom 16:37, 23. Aug. 2009
Zeile 3:		Zeile 3:
	{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}		{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}

-	So sehen wir, dass der Graph der Funktion <math>y = (x-3)^{2} + 2</math> der Graph der Funktion <math>y=x^{2}</math> ist, nur zwei Einheiten nach oben und drei Einheiten nach rechts verschoben ~~(Siehe Sie 8a und 8b)~~.	+	So sehen wir, dass der Graph der Funktion <math>y = (x-3)^{2} + 2</math> der Graph der Funktion <math>y=x^{2}</math> ist, nur zwei Einheiten nach oben und drei Einheiten nach rechts verschoben.

Tek: Replaced figures with metapost figures

Tek — Wed, 19 Aug 2009 12:57:53 GMT

Replaced figures with metapost figures

← Nächstältere Version		Version vom 12:57, 19. Aug. 2009
Zeile 7:		Zeile 7:

	{\| align="center"		{\| align="center"
-	\|align="center"\|~~[[Image~~:~~2_3_8_c-1~~.~~gif\|center]]~~	+	\|align="center"\|{{:2.3.8c - Solution - The parabola y = x²}}
	\|\|		\|\|
-	\|align="center"\|~~[[Image~~:~~2_3_8_c-~~2.~~gif\|center]]~~	+	\|align="center"\|{{:2.3.8c - Solution - The parabola y = x² - 6x + 11}}
	\|-		\|-
	\|align="center"\|<small>Der Graph von ''f''(''x'') = ''x''²</small>		\|align="center"\|<small>Der Graph von ''f''(''x'') = ''x''²</small>

Markus.bez um 14:00, 9. Jun. 2009

Markus.bez — Tue, 09 Jun 2009 14:00:45 GMT

← Nächstältere Version		Version vom 14:00, 9. Jun. 2009
Zeile 3:		Zeile 3:
	{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}		{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}

-	So sehen wir dass der Graph ~~von~~ der Funktion <math>y = (x-3)^{2} + 2</math> der Graph ~~von~~ der Funktion <math>y=x^{2}</math> ist, nur zwei Einheiten nach oben, und drei Einheiten nach rechts verschoben (~~Sehen~~ Sie 8a und 8b).	+	So sehen wir, dass der Graph der Funktion <math>y = (x-3)^{2} + 2</math> der Graph der Funktion <math>y=x^{2}</math> ist, nur zwei Einheiten nach oben und drei Einheiten nach rechts verschoben (Siehe Sie 8a und 8b).


Zeile 11:		Zeile 11:
	\|align="center"\|[[Image:2_3_8_c-2.gif\|center]]		\|align="center"\|[[Image:2_3_8_c-2.gif\|center]]
	\|-		\|-
-	\|align="center"\|<small>~~The graph of~~ ''f''(''x'') = ''x''²</small>	+	\|align="center"\|<small>Der Graph von ''f''(''x'') = ''x''²</small>
	\|\|		\|\|
-	\|align="center"\|<small>~~The graph of~~ ''f''(''x'') = ''x''² - 6x + 11</small>	+	\|align="center"\|<small>Der Graph von ''f''(''x'') = ''x''² - 6x + 11</small>
	\|}		\|}

Martin um 19:29, 16. Mär. 2009

Martin — Mon, 16 Mar 2009 19:29:28 GMT

← Nächstältere Version		Version vom 19:29, 16. Mär. 2009
Zeile 1:		Zeile 1:
-	~~By completing the square, we can rewrite the function as~~	+	Durch quadratische Ergänzung können wir den Ausdruck umschreiben

	{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}		{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}

-	~~and when the function is written in this way, we see that the graph~~ <math>y = (x-3)^{2} + 2</math> ~~is the same curve as the parabola~~ <math>y=x^{2}</math>, ~~but shifted two units up and three units to the right~~ (~~see sub-exercise a and b~~).	+	So sehen wir dass der Graph von der Funktion <math>y = (x-3)^{2} + 2</math> der Graph von der Funktion <math>y=x^{2}</math> ist, nur zwei Einheiten nach oben, und drei Einheiten nach rechts verschoben (Sehen Sie 8a und 8b).

Tekbot: hat „Solution 2.3:8c“ nach „Lösung 2.3:8c“ verschoben: Robot: moved page

Tekbot — Wed, 22 Oct 2008 14:15:05 GMT

hat „Solution 2.3:8c“ nach „Lösung 2.3:8c“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 14:15, 22. Okt. 2008

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

Tekbot — Wed, 22 Oct 2008 08:34:48 GMT

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

← Nächstältere Version		Version vom 08:34, 22. Okt. 2008
Zeile 1:		Zeile 1:
	By completing the square, we can rewrite the function as		By completing the square, we can rewrite the function as

-	{{~~Displayed math~~\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}	+	{{Abgesetzte Formel\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}

	and when the function is written in this way, we see that the graph <math>y = (x-3)^{2} + 2</math> is the same curve as the parabola <math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise a and b).		and when the function is written in this way, we see that the graph <math>y = (x-3)^{2} + 2</math> is the same curve as the parabola <math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise a and b).

Tek um 13:10, 29. Sep. 2008

Tek — Mon, 29 Sep 2008 13:10:22 GMT

← Nächstältere Version		Version vom 13:10, 29. Sep. 2008
Zeile 1:		Zeile 1:
	By completing the square, we can rewrite the function as		By completing the square, we can rewrite the function as

		+	{{Displayed math\|\|<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}}

-	<math>~~f\left( x \right)~~=~~x^{2}-6x+11=\left~~( x-3 ~~\right~~)^{2}~~-3^{~~2~~}+11~~=~~\left(~~ x~~-3 \right)~~^{2}~~+2,~~</math>	+	and when the function is written in this way, we see that the graph <math>y = (x-3)^{2} + 2</math> is the same curve as the parabola <math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise a and b).

-	and when the function is written in this way, we can see that the graph
-	<math>y=\left( x-3 \right)^{2}+2</math>
-	is the same curve as the parabola
-	<math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise d and e).

-		+	{\| align="center"
-	[[Image:2_3_8_c.gif\|center]]	+	\|align="center"\|[[Image:2_3_8_c-1.gif\|center]]
		+	\|\|
		+	\|align="center"\|[[Image:2_3_8_c-2.gif\|center]]
		+	\|-
		+	\|align="center"\|<small>The graph of ''f''(''x'') = ''x''²</small>
		+	\|\|
		+	\|align="center"\|<small>The graph of ''f''(''x'') = ''x''² - 6x + 11</small>
		+	\|}

Ian um 11:36, 21. Sep. 2008

Ian — Sun, 21 Sep 2008 11:36:32 GMT

← Nächstältere Version		Version vom 11:36, 21. Sep. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	By completing the square, we can rewrite the function as
-	<~~center~~> ~~[[Image:2_3_8c.gif]]~~ </~~center~~>	+
-	{~~{NAVCONTENT_STOP}~~}	+
		+	<math>f\left( x \right)=x^{2}-6x+11=\left( x-3 \right)^{2}-3^{2}+11=\left( x-3 \right)^{2}+2,</math>
		+
		+	and when the function is written in this way, we can see that the graph
		+	<math>y=\left( x-3 \right)^{2}+2</math>
		+	is the same curve as the parabola
		+	<math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise d and e).
		+
		+
	[[Image:2_3_8_c.gif\|center]]		[[Image:2_3_8_c.gif\|center]]

Tekbot: Lösning 2.3:8c moved to Solution 2.3:8c: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:04:43 GMT

Lösning 2.3:8c moved to Solution 2.3:8c: Robot: moved page

← Nächstältere Version

Version vom 09:04, 9. Sep. 2008

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

Tekbot — Thu, 21 Aug 2008 06:49:29 GMT

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

← Nächstältere Version		Version vom 06:49, 21. Aug. 2008
Zeile 1:		Zeile 1:
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:2_3_8c.gif]] </center>	+	<center> [[Image:2_3_8c.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}
-	[[~~Bild~~:2_3_8_c.gif\|center]]	+	[[Image:2_3_8_c.gif\|center]]

← Nächstältere Version		Version vom 12:57, 19. Aug. 2009
Zeile 7:		Zeile 7:

	{\| align="center"		{\| align="center"
-	\|align="center"\|~~[[Image~~:~~2_3_8_c-1~~.~~gif\|center]]~~	+	\|align="center"\|{{:2.3.8c - Solution - The parabola y = x²}}
	\|\|		\|\|
-	\|align="center"\|~~[[Image~~:~~2_3_8_c-~~2.~~gif\|center]]~~	+	\|align="center"\|{{:2.3.8c - Solution - The parabola y = x² - 6x + 11}}
	\|-		\|-
	\|align="center"\|<small>Der Graph von ''f''(''x'') = ''x''²</small>		\|align="center"\|<small>Der Graph von ''f''(''x'') = ''x''²</small>