Solution 2.3:8b

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m (Lösning 2.3:8b moved to Solution 2.3:8b: Robot: moved page)
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As a starting point, we can take the curve
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<center> [[Image:2_3_8b.gif]] </center>
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<math>y=x^{2}+2</math>
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which is a parabola with a minimum at
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<math>\left( 0 \right.,\left. 2 \right)</math>
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and is sketched further down. Compared with that curve,
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<math>y=\left( x-1 \right)^{2}+2</math>
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is the same curve in which we must consistently choose
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<math>x</math>
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to be one unit greater in order to get the same
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<math>y</math>
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-value. The curve
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<math>y=\left( x-1 \right)^{2}+2</math>
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is thus shifted one unit to the right compared with
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<math>y=x^{2}+2</math>.
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[[Image:2_3_8_b.gif|center]]
[[Image:2_3_8_b.gif|center]]

Revision as of 11:30, 21 September 2008

As a starting point, we can take the curve \displaystyle y=x^{2}+2 which is a parabola with a minimum at \displaystyle \left( 0 \right.,\left. 2 \right) and is sketched further down. Compared with that curve, \displaystyle y=\left( x-1 \right)^{2}+2 is the same curve in which we must consistently choose \displaystyle x to be one unit greater in order to get the same \displaystyle y -value. The curve \displaystyle y=\left( x-1 \right)^{2}+2 is thus shifted one unit to the right compared with \displaystyle y=x^{2}+2.


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