Solution 2.3:9c - Revision history

Tek at 14:16, 29 September 2008

Tek — Mon, 29 Sep 2008 14:16:37 GMT

←Older revision		Revision as of 14:16, 29 September 2008
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-	To determine all the points on the curve	+	To determine all the points on the curve <math>y=3x^{2}-12x+9</math> which also lie on the ''x''-axis we substitute the equation of the ''x''-axis i.e. <math>y=0</math> in the equation of the curve and obtain that ''x'' must satisfy
-	<math>y=3x^{2}-12x+9</math>	+
-	which also lie on the	+
-	~~<math>~~x~~</math>~~	+
-	-axis we substitute the equation of the	+
-	~~<math>~~x~~</math>~~	+
-	-axis i.e.	+
-	<math>y=0</math>	+
-	in the equation of the curve and obtain that	+
-	~~<math>~~x~~</math>~~	+
-	must satisfy	+

		+	{{Displayed math\|\|<math>0 = 3x^{2}-12x+9\,\textrm{.}</math>}}

-	~~<math>3x^{2}~~-~~12x+9=0</math>~~	+	After dividing by 3 and completing the square the right-hand side is

		+	{{Displayed math\|\|<math>x^{2}-4x+3 = (x-2)^{2} - 2^{2} + 3 = (x-2)^{2} - 1</math>}}

-	~~After dividing by~~	+	and thus the equation has solutions <math>x=2\pm 1,</math>
-	~~<math>3</math>~~	+	i.e. <math>x=2-1=1</math> and <math>x=2+1=3\,</math>.
-	~~and completing the square the right-hand side is~~	+
-		+
-		+
-	~~<math>x^{2}-4x+3=\left( x-2 \right)^{2}-2^{2}+3=\left( x-2 \right)^{2}-1</math>~~	+
-		+
-		+
-	and thus the equation has solutions	+
-		+
-		+
-	<math>x=2\pm 1,</math>	+
-	i.e.	+
-	<math>x=2-1=1</math>	+
-	and	+
-	<math>x=2+1=3~~.</math>~~	+
-		+
-		+
-	~~The points where the curve cut the~~	+
-	~~<math>x</math>~~	+
-	~~-axis are~~	+
-		+
-		+
-	~~<math>~~\~~left( 1 \right.~~,~~\left. 0 \right)~~</math>	+
-	~~and~~	+
-	~~<math>\left( 3 \right~~.~~,\left. 0 \right)</math>~~	+

		+	The points where the curve cut the ''x''-axis are (1,0) and (3,0).


	[[Image:2_3_9_c.gif\|center]]		[[Image:2_3_9_c.gif\|center]]

Ian at 12:11, 21 September 2008

Ian — Sun, 21 Sep 2008 12:11:13 GMT

←Older revision		Revision as of 12:11, 21 September 2008
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-	{~~{NAVCONTENT_START}~~}	+	To determine all the points on the curve
-	<~~center~~> ~~[[Image:2_3_9c~~.~~gif]]~~ </~~center~~>	+	<math>y=3x^{2}-12x+9</math>
-	{{~~NAVCONTENT_STOP~~}}	+	which also lie on the
		+	<math>x</math>
		+	-axis we substitute the equation of the
		+	<math>x</math>
		+	-axis i.e.
		+	<math>y=0</math>
		+	in the equation of the curve and obtain that
		+	<math>x</math>
		+	must satisfy
		+
		+
		+	<math>3x^{2}-12x+9=0</math>
		+
		+
		+	After dividing by
		+	<math>3</math>
		+	and completing the square the right-hand side is
		+
		+
		+	<math>x^{2}-4x+3=\left( x-2 \right)^{2}-2^{2}+3=\left( x-2 \right)^{2}-1</math>
		+
		+
		+	and thus the equation has solutions
		+
		+
		+	<math>x=2\pm 1,</math>
		+	i.e.
		+	<math>x=2-1=1</math>
		+	and
		+	<math>x=2+1=3.</math>
		+
		+
		+	The points where the curve cut the
		+	<math>x</math>
		+	-axis are
		+
		+
		+	<math>\left( 1 \right.,\left. 0 \right)</math>
		+	and
		+	<math>\left( 3 \right.,\left. 0 \right)</math>
		+
		+
		+
	[[Image:2_3_9_c.gif\|center]]		[[Image:2_3_9_c.gif\|center]]

Tekbot: Lösning 2.3:9c moved to Solution 2.3:9c: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:05:43 GMT

Lösning 2.3:9c moved to Solution 2.3:9c: Robot: moved page

←Older revision

Revision as of 09:05, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 06:49:59 GMT

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

←Older revision		Revision as of 06:49, 21 August 2008
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Madde at 11:44, 15 August 2008

Madde — Fri, 15 Aug 2008 11:44:05 GMT

←Older revision		Revision as of 11:44, 15 August 2008
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Oskar: Ny sida: {{NAVCONTENT_START}} Bild:2_3_9c.gif {{NAVCONTENT_STOP}}

Oskar — Tue, 01 Apr 2008 10:29:58 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:2_3_9c.gif </center> {{NAVCONTENT_STOP}}

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