Solution 2.3:8a

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The curve
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The curve <math>y=x^{2}</math> is a parabola with a minimum at the origin according to the figure below on the left and, compared with that curve, <math>y=x^{2}+1</math>
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<math>y=x^{2}</math>
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is the same curve but with the number 1 added to the ''y''-coordinate of each point, i.e. the parabola is shifted one unit up in the ''y''-direction.
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is a parabola with a minimum at the origin according to the figure below on the left and, compared with that curve,
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<math>y=x^{2}+1</math>
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is the same curve but with the number
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<math>1</math>
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added to the
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<math>y</math>
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-coordinate of each point, i.e. the parabola is shifted one unit up in the
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<math>y</math>
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-direction.
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[[Image:2_3_8_a.gif|center]]
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{| align="center"
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|align="center"|[[Image:2_3_8_a-1.gif|center]]
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| width="10px"|&nbsp;
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|align="center"|[[Image:2_3_8_a-1.gif|center]]
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|-
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|align="center"|<small>The graph of ''f''(''x'')&nbsp;=&nbsp;''x''²</small>
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||
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|align="center"|<small>The graph of ''f''(''x'')&nbsp;=&nbsp;''x''²&nbsp;+&nbsp;1</small>
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|}

Revision as of 12:29, 29 September 2008

The curve \displaystyle y=x^{2} is a parabola with a minimum at the origin according to the figure below on the left and, compared with that curve, \displaystyle y=x^{2}+1 is the same curve but with the number 1 added to the y-coordinate of each point, i.e. the parabola is shifted one unit up in the y-direction.


 
The graph of f(x) = x² The graph of f(x) = x² + 1
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