Lösung 2.3:6b - Versionsgeschichte

Markus.bez um 13:55, 9. Jun. 2009

2009-06-09T13:55:38Z

← Nächstältere Version		Version vom 13:55, 9. Jun. 2009
Zeile 1:		Zeile 1:
-	Indem wir quadratische Ergänzung benutzen, können wir danach einfach den kleinsten ~~wert~~ der Funktion finden,	+	Indem wir quadratische Ergänzung benutzen, können wir danach einfach den kleinsten Wert der Funktion finden,

	{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}

	Nachdem <math>(x-2)^{2}</math> immer grösser als oder gleich null ist, ist der kleinste Wert des Ausdruckes -2, wenn <math>x-2=0</math>, also <math>x=2</math> ist.		Nachdem <math>(x-2)^{2}</math> immer grösser als oder gleich null ist, ist der kleinste Wert des Ausdruckes -2, wenn <math>x-2=0</math>, also <math>x=2</math> ist.

2009-03-16T17:40:16Z

← Nächstältere Version		Version vom 17:40, 16. Mär. 2009
Zeile 3:		Zeile 3:
	{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}

-	Nachdem <math>(x-2)^{2}</math> immer grösser als oder gleich null ist, ist der kleinste Wert des Ausdruckes -2, wenn <math>x-2=0</math>, also <math>x=2</math>.	+	Nachdem <math>(x-2)^{2}</math> immer grösser als oder gleich null ist, ist der kleinste Wert des Ausdruckes -2, wenn <math>x-2=0</math>, also <math>x=2</math> ist.

2009-03-16T17:39:55Z

← Nächstältere Version		Version vom 17:39, 16. Mär. 2009
Zeile 1:		Zeile 1:
-	~~By completing the square~~, ~~the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value~~,	+	Indem wir quadratische Ergänzung benutzen, können wir danach einfach den kleinsten wert der Funktion finden,

	{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}

-	~~Because~~ <math>(x-2)^{2}</math> ~~is a quadratic~~, ~~this term is always larger than or equal to 0 and the whole expression is therefore at least equal to~~ -2, ~~which occurs when~~ <math>x-2=0</math> ~~and the quadratic is zero~~, ~~i.e.~~ <math>x=2</math>.	+	Nachdem <math>(x-2)^{2}</math> immer grösser als oder gleich null ist, ist der kleinste Wert des Ausdruckes -2, wenn <math>x-2=0</math>, also <math>x=2</math>.

2008-10-22T14:12:45Z

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

← Nächstältere Version

Version vom 14:12, 22. Okt. 2008

2008-10-22T08:34:08Z

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, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,		By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,

-	{{~~Displayed math~~\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}

	Because <math>(x-2)^{2}</math> is a quadratic, this term is always larger than or equal to 0 and the whole expression is therefore at least equal to -2, which occurs when <math>x-2=0</math> and the quadratic is zero, i.e. <math>x=2</math>.		Because <math>(x-2)^{2}</math> is a quadratic, this term is always larger than or equal to 0 and the whole expression is therefore at least equal to -2, which occurs when <math>x-2=0</math> and the quadratic is zero, i.e. <math>x=2</math>.

2008-09-29T11:34:05Z

← Nächstältere Version		Version vom 11:34, 29. Sep. 2008
Zeile 1:		Zeile 1:
	By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,		By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,

		+	{{Displayed math\|\|<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}}

-	~~<math>x^{2}-4x+2=\left( x-2 \right)^{2}-2^{2}+2=\left( x-2 \right)^{2}-2</math>~~	+	Because <math>(x-2)^{2}</math> is a quadratic, this term is always larger than or equal to 0 and the whole expression is therefore at least equal to -2, which occurs when <math>x-2=0</math> and the quadratic is zero, i.e. <math>x=2</math>.
-		+
-		+
-	Because	+
-	<math>~~\left~~( x-2 ~~\right~~)^{2}</math>	+
-	is a quadratic, this term is always larger than or equal to	+
-	~~<math>~~0~~</math>~~	+
-	and the whole expression is therefore at least equal to	+
-	~~<math>~~-~~\text{~~2~~}</math>~~, which occurs when	+
-	<math>x-~~\text{~~2}=0~~\text{ }~~</math>	+
-	and the quadratic is zero, i.e.	+
-	<math>x=~~\text{~~2}</math>.	+

2008-09-21T10:56:39Z

← Nächstältere Version		Version vom 10:56, 21. Sep. 2008
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-	{{~~NAVCONTENT_START~~}}	+	By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,
-	<~~center~~> ~~[[Image:2_3_6b.gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+
		+	<math>x^{2}-4x+2=\left( x-2 \right)^{2}-2^{2}+2=\left( x-2 \right)^{2}-2</math>
		+
		+
		+	Because
		+	<math>\left( x-2 \right)^{2}</math>
		+	is a quadratic, this term is always larger than or equal to
		+	<math>0</math>
		+	and the whole expression is therefore at least equal to
		+	<math>-\text{2}</math>, which occurs when
		+	<math>x-\text{2}=0\text{ }</math>
		+	and the quadratic is zero, i.e.
		+	<math>x=\text{2}</math>.

2008-09-09T09:02:23Z

← Nächstältere Version

Version vom 09:02, 9. Sep. 2008

2008-08-21T06:48:19Z

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

2008-04-01T10:13:19Z

Ny sida: {{NAVCONTENT_START}} <center> Bild:2_3_6b.gif </center> {{NAVCONTENT_STOP}}

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