Question 150596
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In order to graph {{{y=x^2+2x-15}}}, we need to plot some points.



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




{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(-4)^2+2(-4)-15}}} Plug in {{{x=-4}}}.



{{{y=1(16)+2(-4)-15}}} Square {{{-4}}} to get {{{16}}}.



{{{y=16+2(-4)-15}}} Multiply {{{1}}} and {{{16}}} to get {{{16}}}.



{{{y=16-8-15}}} Multiply {{{2}}} and {{{-4}}} to get {{{-8}}}.



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



So when {{{x=-4}}}, then {{{y=-7}}}.



So we have the point *[Tex \LARGE \left(-4,-7\right)].



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



{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(-3)^2+2(-3)-15}}} Plug in {{{x=-3}}}.



{{{y=1(9)+2(-3)-15}}} Square {{{-3}}} to get {{{9}}}.



{{{y=9+2(-3)-15}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=9-6-15}}} Multiply {{{2}}} and {{{-3}}} to get {{{-6}}}.



{{{y=-12}}} Combine like terms.



So when {{{x=-3}}}, then {{{y=-12}}}.



So we have the point *[Tex \LARGE \left(-3,-12\right)].



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



{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(-2)^2+2(-2)-15}}} Plug in {{{x=-2}}}.



{{{y=1(4)+2(-2)-15}}} Square {{{-2}}} to get {{{4}}}.



{{{y=4+2(-2)-15}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=4-4-15}}} Multiply {{{2}}} and {{{-2}}} to get {{{-4}}}.



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



{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(-1)^2+2(-1)-15}}} Plug in {{{x=-1}}}.



{{{y=1(1)+2(-1)-15}}} Square {{{-1}}} to get {{{1}}}.



{{{y=1+2(-1)-15}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1-2-15}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}.



{{{y=-16}}} Combine like terms.



So when {{{x=-1}}}, then {{{y=-16}}}.



So we have the point *[Tex \LARGE \left(-1,-16\right)].



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



{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(0)^2+2(0)-15}}} Plug in {{{x=0}}}.



{{{y=1(0)+2(0)-15}}} Square {{{0}}} to get {{{0}}}.



{{{y=0+2(0)-15}}} Multiply {{{1}}} and {{{0}}} to get {{{0}}}.



{{{y=0+0-15}}} Multiply {{{2}}} and {{{0}}} to get {{{0}}}.



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



So when {{{x=0}}}, then {{{y=-15}}}.



So we have the point *[Tex \LARGE \left(0,-15\right)].



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



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



{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(1)^2+2(1)-15}}} Plug in {{{x=1}}}.



{{{y=1(1)+2(1)-15}}} Square {{{1}}} to get {{{1}}}.



{{{y=1+2(1)-15}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1+2-15}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}.



{{{y=-12}}} Combine like terms.



So when {{{x=1}}}, then {{{y=-12}}}.



So we have the point *[Tex \LARGE \left(1,-12\right)].



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



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



{{{y=x^2+2x-15}}} Start with the given equation.



{{{y=(2)^2+2(2)-15}}} Plug in {{{x=2}}}.



{{{y=1(4)+2(2)-15}}} Square {{{2}}} to get {{{4}}}.



{{{y=4+2(2)-15}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=4+4-15}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}.



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



So when {{{x=2}}}, then {{{y=-7}}}.



So we have the point *[Tex \LARGE \left(2,-7\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>-4</td><td>-7</td></tr>
<tr><td>-3</td><td>-12</td></tr>
<tr><td>-2</td><td>-15</td></tr>
<tr><td>-1</td><td>-16</td></tr>
<tr><td>0</td><td>-15</td></tr>
<tr><td>1</td><td>-12</td></tr>
<tr><td>2</td><td>-7</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -10, 10, -20, 10,
grid(1),
graph(900, 900, -10, 10, -20, 10, 0),
circle(-4,-7,0.08),circle(-4,-7,0.10),
circle(-3,-12,0.08),circle(-3,-12,0.10),
circle(-2,-15,0.08),circle(-2,-15,0.10),
circle(-1,-16,0.08),circle(-1,-16,0.10),
circle(0,-15,0.08),circle(0,-15,0.10),
circle(1,-12,0.08),circle(1,-12,0.10),
circle(2,-7,0.08),circle(2,-7,0.10)

)}}}


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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=x^2+2x-15}}}:



{{{ drawing(900, 900, -10, 10, -20, 10,
grid(1),
graph(900, 900, -10, 10, -20, 10, x^2+2x-15),
circle(-4,-7,0.08),circle(-4,-7,0.10),
circle(-3,-12,0.08),circle(-3,-12,0.10),
circle(-2,-15,0.08),circle(-2,-15,0.10),
circle(-1,-16,0.08),circle(-1,-16,0.10),
circle(0,-15,0.08),circle(0,-15,0.10),
circle(1,-12,0.08),circle(1,-12,0.10),
circle(2,-7,0.08),circle(2,-7,0.10)

)}}} Graph of {{{y=x^2+2x-15}}}