Solution 2.3:8c

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m (Lösning 2.3:8c moved to Solution 2.3:8c: Robot: moved page)
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By completing the square, we can rewrite the function as
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<center> [[Image:2_3_8c.gif]] </center>
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<math>f\left( x \right)=x^{2}-6x+11=\left( x-3 \right)^{2}-3^{2}+11=\left( x-3 \right)^{2}+2,</math>
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and when the function is written in this way, we can see that the graph
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<math>y=\left( x-3 \right)^{2}+2</math>
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is the same curve as the parabola
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<math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise d and e).
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[[Image:2_3_8_c.gif|center]]
[[Image:2_3_8_c.gif|center]]

Revision as of 11:36, 21 September 2008

By completing the square, we can rewrite the function as


\displaystyle f\left( x \right)=x^{2}-6x+11=\left( x-3 \right)^{2}-3^{2}+11=\left( x-3 \right)^{2}+2,

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


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