Question 150921


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In order to graph {{{y=x^2-3}}}, we need to plot some points.



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

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



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(9)-3}}} Square {{{-3}}} to get {{{9}}}.



{{{y=9-3}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=6}}} Combine like terms.



So when {{{x=-3}}}, then {{{y=6}}}.



So we have the point *[Tex \LARGE \left(-3,6\right)].



----------------------------------------------------



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



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(4)-3}}} Square {{{-2}}} to get {{{4}}}.



{{{y=4-3}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=1}}} Combine like terms.



So when {{{x=-2}}}, then {{{y=1}}}.



So we have the point *[Tex \LARGE \left(-2,1\right)].



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



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(1)-3}}} Square {{{-1}}} to get {{{1}}}.



{{{y=1-3}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=-2}}} Combine like terms.



So when {{{x=-1}}}, then {{{y=-2}}}.



So we have the point *[Tex \LARGE \left(-1,-2\right)].



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Let's find y when {{{x=0}}}:



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(0)-3}}} Square {{{0}}} to get {{{0}}}.



{{{y=0-3}}} Multiply {{{1}}} and {{{0}}} to get {{{0}}}.



{{{y=-3}}} Combine like terms.



So when {{{x=0}}}, then {{{y=-3}}}.



So we have the point *[Tex \LARGE \left(0,-3\right)].



----------------------------------------------------



Let's find y when {{{x=1}}}:



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(1)-3}}} Square {{{1}}} to get {{{1}}}.



{{{y=1-3}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=-2}}} Combine like terms.



So when {{{x=1}}}, then {{{y=-2}}}.



So we have the point *[Tex \LARGE \left(1,-2\right)].



----------------------------------------------------



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



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(4)-3}}} Square {{{2}}} to get {{{4}}}.



{{{y=4-3}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=1}}} Combine like terms.



So when {{{x=2}}}, then {{{y=1}}}.



So we have the point *[Tex \LARGE \left(2,1\right)].



----------------------------------------------------



Let's find y when {{{x=3}}}:



{{{y=x^2-3}}} Start with the given equation.



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



{{{y=1(9)-3}}} Square {{{3}}} to get {{{9}}}.



{{{y=9-3}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=6}}} Combine like terms.



So when {{{x=3}}}, then {{{y=6}}}.



So we have the point *[Tex \LARGE \left(3,6\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>-3</td><td>6</td></tr>
<tr><td>-2</td><td>1</td></tr>
<tr><td>-1</td><td>-2</td></tr>
<tr><td>0</td><td>-3</td></tr>
<tr><td>1</td><td>-2</td></tr>
<tr><td>2</td><td>1</td></tr>
<tr><td>3</td><td>6</td></tr>
</TABLE>

</pre>

Now let's plot the points:



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

)}}}


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<h4>Graph:</h4>

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



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

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