Question 219630
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Table of Contents:


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In order to graph {{{y=x^2}}}, we need to plot a few points. To find these points, simply plug in values of 'x' to find corresponding values of 'y'. They will form the points in the form (x,y).



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



{{{y=x^2}}} Start with the given equation.



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



{{{y=9}}} Square -3 to get 9.



So when {{{x=-3}}}, {{{y=9}}}. So we have the point (-3,9).



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



{{{y=x^2}}} Start with the given equation.



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



{{{y=4}}} Square -2 to get 4.



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



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



{{{y=x^2}}} Start with the given equation.



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



{{{y=1}}} Square -1 to get 1.



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



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Let's find the y value when {{{x=0}}}



{{{y=x^2}}} Start with the given equation.



{{{y=(0)^2}}} Plug in {{{x=0}}}.



{{{y=0}}} Square 0 to get 0.



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



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



{{{y=x^2}}} Start with the given equation.



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



{{{y=1}}} Square 1 to get 1.



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



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



{{{y=x^2}}} Start with the given equation.



{{{y=(2)^2}}} Plug in {{{x=2}}}.



{{{y=4}}} Square 2 to get 4.



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



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



{{{y=x^2}}} Start with the given equation.



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



{{{y=9}}} Square 3 to get 9.



So when {{{x=3}}}, {{{y=9}}}. So we have the point (3,9).



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



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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>-3</td><td>9</td></tr>
<tr><td>-2</td><td>4</td></tr>
<tr><td>-1</td><td>1</td></tr>
<tr><td>0</td><td>0</td></tr>
<tr><td>1</td><td>1</td></tr>
<tr><td>2</td><td>4</td></tr>
<tr><td>3</td><td>9</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(500, 500, -10, 10, -10, 10,
grid(1),
graph(500, 500, -10, 10, -10, 10, 0),
circle(-3,9,0.08),circle(-3,9,0.10),
circle(-2,4,0.08),circle(-2,4,0.10),
circle(-1,1,0.08),circle(-1,1,0.10),
circle(0,0,0.08),circle(0,0,0.10),
circle(1,1,0.08),circle(1,1,0.10),
circle(2,4,0.08),circle(2,4,0.10),
circle(3,9,0.08),circle(3,9,0.10)

)}}}


Now draw a curve through all of the points to graph {{{y=x^2}}}:



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{{{ drawing(500, 500, -10, 10, -10, 10,
grid(1),
graph(500, 500, -10, 10, -10, 10, x^2),
circle(-3,9,0.08),circle(-3,9,0.10),
circle(-2,4,0.08),circle(-2,4,0.10),
circle(-1,1,0.08),circle(-1,1,0.10),
circle(0,0,0.08),circle(0,0,0.10),
circle(1,1,0.08),circle(1,1,0.10),
circle(2,4,0.08),circle(2,4,0.10),
circle(3,9,0.08),circle(3,9,0.10)

)}}} Graph of {{{y=x^2}}}


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