Question 147611


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



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



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



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



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



{{{y=4-2(-2)-2}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=4+4-2}}} Multiply {{{-2}}} and {{{-2}}} to get {{{4}}}.



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



So if {{{x=-2}}}, then {{{y=6}}}.



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



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



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



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



{{{y=1-2(-1)-2}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1+2-2}}} Multiply {{{-2}}} and {{{-1}}} to get {{{2}}}.



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



So if {{{x=-1}}}, then {{{y=1}}}.



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

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



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



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



{{{y=1(0)-2(0)-2}}} Square {{{0}}} to get {{{0}}}.



{{{y=0-2(0)-2}}} Multiply {{{1}}} and {{{0}}} to get {{{0}}}.



{{{y=0+0-2}}} Multiply {{{-2}}} and {{{0}}} to get {{{0}}}.



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



So if {{{x=0}}}, then {{{y=-2}}}.



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



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



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



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



{{{y=1-2(1)-2}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1-2-2}}} Multiply {{{-2}}} and {{{1}}} to get {{{-2}}}.



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



So if {{{x=1}}}, then {{{y=-3}}}.



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



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



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



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



{{{y=4-2(2)-2}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=4-4-2}}} Multiply {{{-2}}} and {{{2}}} to get {{{-4}}}.



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



So if {{{x=2}}}, then {{{y=-2}}}.



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



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



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



{{{y=1(9)-2(3)-2}}} Square {{{3}}} to get {{{9}}}.



{{{y=9-2(3)-2}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=9-6-2}}} Multiply {{{-2}}} and {{{3}}} to get {{{-6}}}.



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



So if {{{x=3}}}, then {{{y=1}}}.



Let's find y when {{{x=4}}}:



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



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



{{{y=1(16)-2(4)-2}}} Square {{{4}}} to get {{{16}}}.



{{{y=16-2(4)-2}}} Multiply {{{1}}} and {{{16}}} to get {{{16}}}.



{{{y=16-8-2}}} Multiply {{{-2}}} and {{{4}}} to get {{{-8}}}.



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



So if {{{x=4}}}, then {{{y=6}}}.



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



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



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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>6</td></tr>
<tr><td>-1</td><td>1</td></tr>
<tr><td>0</td><td>-2</td></tr>
<tr><td>1</td><td>-3</td></tr>
<tr><td>2</td><td>-2</td></tr>
<tr><td>3</td><td>1</td></tr>
<tr><td>4</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(-2,6,0.08),circle(-2,6,0.10),
circle(-1,1,0.08),circle(-1,1,0.10),
circle(0,-2,0.08),circle(0,-2,0.10),
circle(1,-3,0.08),circle(1,-3,0.10),
circle(2,-2,0.08),circle(2,-2,0.10),
circle(3,1,0.08),circle(3,1,0.10),
circle(4,6,0.08),circle(4,6,0.10)

)}}}


<a name="graph">



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



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

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