Question 150929

Table of Contents:
<a name="top">
<a href="#table">Table</a>

<a href="#graph">Graph</a>


In order to graph {{{y=(x-3)^2 + 1}}}, we need to plot a few points.



Let's find the y value when {{{x=0}}} note: you can start at any x value. 



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(0-3)^2 + 1}}} Plug in {{{x=0}}}.



{{{y=10}}} Simplify.



So when {{{x=0}}}, {{{y=10}}}. So we have the point (0,10).



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Let's find the y value when {{{x=1}}}  



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(1-3)^2 + 1}}} Plug in {{{x=1}}}.



{{{y=5}}} Simplify.



So when {{{x=1}}}, {{{y=5}}}. So we have the point (1,5).



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Let's find the y value when {{{x=2}}}  



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(2-3)^2 + 1}}} Plug in {{{x=2}}}.



{{{y=2}}} Simplify.



So when {{{x=2}}}, {{{y=2}}}. So we have the point (2,2).



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Let's find the y value when {{{x=3}}}  



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(3-3)^2 + 1}}} Plug in {{{x=3}}}.



{{{y=1}}} Simplify.



So when {{{x=3}}}, {{{y=1}}}. So we have the point (3,1).



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Let's find the y value when {{{x=4}}}  



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(4-3)^2 + 1}}} Plug in {{{x=4}}}.



{{{y=2}}} Simplify.



So when {{{x=4}}}, {{{y=2}}}. So we have the point (4,2).



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Let's find the y value when {{{x=5}}}  



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(5-3)^2 + 1}}} Plug in {{{x=5}}}.



{{{y=5}}} Simplify.



So when {{{x=5}}}, {{{y=5}}}. So we have the point (5,5).



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Let's find the y value when {{{x=6}}}  



{{{y=(x-3)^2 + 1}}} Start with the given equation.



{{{y=(6-3)^2 + 1}}} Plug in {{{x=6}}}.



{{{y=10}}} Simplify.



So when {{{x=6}}}, {{{y=10}}}. So we have the point (6,10).



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Now let's make a table of the values we just found.



<a name="table">



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<h4>Table of Values:</h4><pre>

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR><tr><td>0</td><td>10</td></tr>
<tr><td>1</td><td>5</td></tr>
<tr><td>2</td><td>2</td></tr>
<tr><td>3</td><td>1</td></tr>
<tr><td>4</td><td>2</td></tr>
<tr><td>5</td><td>5</td></tr>
<tr><td>6</td><td>10</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -12, 12, -12, 12,
grid(1),
graph(900, 900, -12, 12, -12, 12, 0),
circle(0,10,0.08),circle(0,10,0.10),
circle(1,5,0.08),circle(1,5,0.10),
circle(2,2,0.08),circle(2,2,0.10),
circle(3,1,0.08),circle(3,1,0.10),
circle(4,2,0.08),circle(4,2,0.10),
circle(5,5,0.08),circle(5,5,0.10),
circle(6,10,0.08),circle(6,10,0.10)

)}}}


<a name="graph">



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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=(x-3)^2 + 1}}}:



{{{ drawing(900, 900, -12, 12, -12, 12,
grid(1),
graph(900, 900, -12, 12, -12, 12, (x-3)^2 + 1),
circle(0,10,0.08),circle(0,10,0.10),
circle(1,5,0.08),circle(1,5,0.10),
circle(2,2,0.08),circle(2,2,0.10),
circle(3,1,0.08),circle(3,1,0.10),
circle(4,2,0.08),circle(4,2,0.10),
circle(5,5,0.08),circle(5,5,0.10),
circle(6,10,0.08),circle(6,10,0.10)

)}}} Graph of {{{y=(x-3)^2 + 1}}}