Question 152928


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In order to graph {{{y=-3x^2+x-5}}}, we need to plot some points.



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

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



{{{y=-3x^2+x-5}}} Start with the given equation.



{{{y=-3(-2)^2+-2-5}}} Plug in {{{x=-2}}}.



{{{y=-3(4)-2-5}}} Square {{{-2}}} to get {{{4}}}.



{{{y=-12-2-5}}} Multiply {{{-3}}} and {{{4}}} to get {{{-12}}}.



{{{y=-19}}} Combine like terms.



So when {{{x=-2}}}, then {{{y=-19}}}.



So we have the point *[Tex \LARGE \left(-2,-19\right)].



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



{{{y=-3x^2+x-5}}} Start with the given equation.



{{{y=-3(-1)^2+-1-5}}} Plug in {{{x=-1}}}.



{{{y=-3(1)-1-5}}} Square {{{-1}}} to get {{{1}}}.



{{{y=-3-1-5}}} Multiply {{{-3}}} and {{{1}}} to get {{{-3}}}.



{{{y=-9}}} Combine like terms.



So when {{{x=-1}}}, then {{{y=-9}}}.



So we have the point *[Tex \LARGE \left(-1,-9\right)].



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



{{{y=-3x^2+x-5}}} Start with the given equation.



{{{y=-3(0)^2+0-5}}} Plug in {{{x=0}}}.



{{{y=-3(0)+0-5}}} Square {{{0}}} to get {{{0}}}.



{{{y=0+0-5}}} Multiply {{{-3}}} and {{{0}}} to get {{{0}}}.



{{{y=-5}}} Combine like terms.



So when {{{x=0}}}, then {{{y=-5}}}.



So we have the point *[Tex \LARGE \left(0,-5\right)].



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



{{{y=-3x^2+x-5}}} Start with the given equation.



{{{y=-3(1)^2+1-5}}} Plug in {{{x=1}}}.



{{{y=-3(1)+1-5}}} Square {{{1}}} to get {{{1}}}.



{{{y=-3+1-5}}} Multiply {{{-3}}} and {{{1}}} to get {{{-3}}}.



{{{y=-7}}} Combine like terms.



So when {{{x=1}}}, then {{{y=-7}}}.



So we have the point *[Tex \LARGE \left(1,-7\right)].



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



{{{y=-3x^2+x-5}}} Start with the given equation.



{{{y=-3(2)^2+2-5}}} Plug in {{{x=2}}}.



{{{y=-3(4)+2-5}}} Square {{{2}}} to get {{{4}}}.



{{{y=-12+2-5}}} Multiply {{{-3}}} and {{{4}}} to get {{{-12}}}.



{{{y=-15}}} Combine like terms.



So when {{{x=2}}}, then {{{y=-15}}}.



So we have the point *[Tex \LARGE \left(2,-15\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>-19</td></tr>
<tr><td>-1</td><td>-9</td></tr>
<tr><td>0</td><td>-5</td></tr>
<tr><td>1</td><td>-7</td></tr>
<tr><td>2</td><td>-15</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -10, 10, -21, 2,
grid(1),
graph(900, 900, -10, 10, -21, 2, 0),
circle(-2,-19,0.08),circle(-2,-19,0.10),
circle(-1,-9,0.08),circle(-1,-9,0.10),
circle(0,-5,0.08),circle(0,-5,0.10),
circle(1,-7,0.08),circle(1,-7,0.10),
circle(2,-15,0.08),circle(2,-15,0.10)

)}}}


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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=-3x^2+x-5}}}:



{{{ drawing(900, 900, -10, 10, -21, 2,
grid(1),
graph(900, 900, -10, 10, -21, 2, -3x^2+x-5),
circle(-2,-19,0.08),circle(-2,-19,0.10),
circle(-1,-9,0.08),circle(-1,-9,0.10),
circle(0,-5,0.08),circle(0,-5,0.10),
circle(1,-7,0.08),circle(1,-7,0.10),
circle(2,-15,0.08),circle(2,-15,0.10)

)}}} Graph of {{{y=-3x^2+x-5}}}