Question 170006
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In order to graph {{{y=x^2}}}, we need to plot some points.



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

(Note: you can start with any x-value):



{{{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}}}, then {{{y=4}}}.



So we have the point *[Tex \LARGE \left(-2,4\right)].



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Let's find y 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}}}, then {{{y=1}}}.



So we have the point *[Tex \LARGE \left(-1,1\right)].



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Let's find y 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}}}, then {{{y=0}}}.



So we have the point *[Tex \LARGE \left(0,0\right)].



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Let's find y 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}}}, then {{{y=1}}}.



So we have the point *[Tex \LARGE \left(1,1\right)].



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Let's find y 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}}}, then {{{y=4}}}.



So we have the point *[Tex \LARGE \left(2,4\right)].



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



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

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</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>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(500, 500, -5, 5, -5, 5,
grid(1),
graph(500, 500, -5, 5, -5, 5, 0),
circle(-2,4,0.05),circle(-2,4,0.08),
circle(-1,1,0.05),circle(-1,1,0.08),
circle(0,0,0.05),circle(0,0,0.08),
circle(1,1,0.05),circle(1,1,0.08),
circle(2,4,0.05),circle(2,4,0.08)

)}}}


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<h4>Graph:</h4>

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



{{{ drawing(500, 500, -5, 5, -5, 5,
grid(1),
graph(500, 500, -5, 5, -5, 5, x^2),
circle(-2,4,0.05),circle(-2,4,0.08),
circle(-1,1,0.05),circle(-1,1,0.08),
circle(0,0,0.05),circle(0,0,0.08),
circle(1,1,0.05),circle(1,1,0.08),
circle(2,4,0.05),circle(2,4,0.08)

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