Question 173351
Do you want to graph this? Please post full instructions.





<a name="top">Table of Contents:



<a href="#table">Jump to Table</a>

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



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



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

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



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



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



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



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



So when {{{x=-2}}}, then {{{y=-8}}}.



So we have the point *[Tex \LARGE \left(-2,-8\right)].



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



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



So when {{{x=2}}}, then {{{y=-8}}}.



So we have the point *[Tex \LARGE \left(2,-8\right)].



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



<a name="table">



<a href="#top">Jump to Top of Page</a>

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>-8</td></tr>
<tr><td>-1</td><td>-2</td></tr>
<tr><td>0</td><td>0</td></tr>
<tr><td>1</td><td>-2</td></tr>
<tr><td>2</td><td>-8</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(-2,-8,0.08),circle(-2,-8,0.10),
circle(-1,-2,0.08),circle(-1,-2,0.10),
circle(0,0,0.08),circle(0,0,0.10),
circle(1,-2,0.08),circle(1,-2,0.10),
circle(2,-8,0.08),circle(2,-8,0.10)

)}}}


<a name="graph">



<a href="#top">Jump to Top of Page</a>

<h4>Graph:</h4>

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



{{{ drawing(500, 500, -10, 10, -10, 10,
grid(1),
graph(500, 500, -10, 10, -10, 10, -2x^2),
circle(-2,-8,0.08),circle(-2,-8,0.10),
circle(-1,-2,0.08),circle(-1,-2,0.10),
circle(0,0,0.08),circle(0,0,0.10),
circle(1,-2,0.08),circle(1,-2,0.10),
circle(2,-8,0.08),circle(2,-8,0.10)

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