Question 316651


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In order to graph {{{y=x^2-8x+7}}}, we need to plot some points.



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

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



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(0)^2-8(0)+7}}} Plug in {{{x=0}}}.



{{{y=1(0)-8(0)+7}}} Square {{{0}}} to get {{{0}}}.



{{{y=0-8(0)+7}}} Multiply {{{1}}} and {{{0}}} to get {{{0}}}.



{{{y=0+0+7}}} Multiply {{{-8}}} and {{{0}}} to get {{{0}}}.



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



So when {{{x=0}}}, then {{{y=7}}}.



So we have the point *[Tex \LARGE \left(0,7\right)].



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



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(1)^2-8(1)+7}}} Plug in {{{x=1}}}.



{{{y=1(1)-8(1)+7}}} Square {{{1}}} to get {{{1}}}.



{{{y=1-8(1)+7}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1-8+7}}} Multiply {{{-8}}} and {{{1}}} to get {{{-8}}}.



{{{y=0}}} Combine like terms.



So when {{{x=1}}}, then {{{y=0}}}.



So we have the point *[Tex \LARGE \left(1,0\right)].



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



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(2)^2-8(2)+7}}} Plug in {{{x=2}}}.



{{{y=1(4)-8(2)+7}}} Square {{{2}}} to get {{{4}}}.



{{{y=4-8(2)+7}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=4-16+7}}} Multiply {{{-8}}} and {{{2}}} to get {{{-16}}}.



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



So when {{{x=2}}}, then {{{y=-5}}}.



So we have the point *[Tex \LARGE \left(2,-5\right)].



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



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



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(3)^2-8(3)+7}}} Plug in {{{x=3}}}.



{{{y=1(9)-8(3)+7}}} Square {{{3}}} to get {{{9}}}.



{{{y=9-8(3)+7}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=9-24+7}}} Multiply {{{-8}}} and {{{3}}} to get {{{-24}}}.



{{{y=-8}}} Combine like terms.



So when {{{x=3}}}, then {{{y=-8}}}.



So we have the point *[Tex \LARGE \left(3,-8\right)].



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



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(4)^2-8(4)+7}}} Plug in {{{x=4}}}.



{{{y=1(16)-8(4)+7}}} Square {{{4}}} to get {{{16}}}.



{{{y=16-8(4)+7}}} Multiply {{{1}}} and {{{16}}} to get {{{16}}}.



{{{y=16-32+7}}} Multiply {{{-8}}} and {{{4}}} to get {{{-32}}}.



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



So when {{{x=4}}}, then {{{y=-9}}}.



So we have the point *[Tex \LARGE \left(4,-9\right)].



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



Let's find y when {{{x=5}}}:



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(5)^2-8(5)+7}}} Plug in {{{x=5}}}.



{{{y=1(25)-8(5)+7}}} Square {{{5}}} to get {{{25}}}.



{{{y=25-8(5)+7}}} Multiply {{{1}}} and {{{25}}} to get {{{25}}}.



{{{y=25-40+7}}} Multiply {{{-8}}} and {{{5}}} to get {{{-40}}}.



{{{y=-8}}} Combine like terms.



So when {{{x=5}}}, then {{{y=-8}}}.



So we have the point *[Tex \LARGE \left(5,-8\right)].



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



Let's find y when {{{x=6}}}:



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(6)^2-8(6)+7}}} Plug in {{{x=6}}}.



{{{y=1(36)-8(6)+7}}} Square {{{6}}} to get {{{36}}}.



{{{y=36-8(6)+7}}} Multiply {{{1}}} and {{{36}}} to get {{{36}}}.



{{{y=36-48+7}}} Multiply {{{-8}}} and {{{6}}} to get {{{-48}}}.



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



So when {{{x=6}}}, then {{{y=-5}}}.



So we have the point *[Tex \LARGE \left(6,-5\right)].



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



Let's find y when {{{x=7}}}:



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(7)^2-8(7)+7}}} Plug in {{{x=7}}}.



{{{y=1(49)-8(7)+7}}} Square {{{7}}} to get {{{49}}}.



{{{y=49-8(7)+7}}} Multiply {{{1}}} and {{{49}}} to get {{{49}}}.



{{{y=49-56+7}}} Multiply {{{-8}}} and {{{7}}} to get {{{-56}}}.



{{{y=0}}} Combine like terms.



So when {{{x=7}}}, then {{{y=0}}}.



So we have the point *[Tex \LARGE \left(7,0\right)].



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



Let's find y when {{{x=8}}}:



{{{y=x^2-8x+7}}} Start with the given equation.



{{{y=(8)^2-8(8)+7}}} Plug in {{{x=8}}}.



{{{y=1(64)-8(8)+7}}} Square {{{8}}} to get {{{64}}}.



{{{y=64-8(8)+7}}} Multiply {{{1}}} and {{{64}}} to get {{{64}}}.



{{{y=64-64+7}}} Multiply {{{-8}}} and {{{8}}} to get {{{-64}}}.



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



So when {{{x=8}}}, then {{{y=7}}}.



So we have the point *[Tex \LARGE \left(8,7\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>0</td><td>7</td></tr>
<tr><td>1</td><td>0</td></tr>
<tr><td>2</td><td>-5</td></tr>
<tr><td>3</td><td>-8</td></tr>
<tr><td>4</td><td>-9</td></tr>
<tr><td>5</td><td>-8</td></tr>
<tr><td>6</td><td>-5</td></tr>
<tr><td>7</td><td>0</td></tr>
<tr><td>8</td><td>7</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(0,7,0.08),circle(0,7,0.10),
circle(1,0,0.08),circle(1,0,0.10),
circle(2,-5,0.08),circle(2,-5,0.10),
circle(3,-8,0.08),circle(3,-8,0.10),
circle(4,-9,0.08),circle(4,-9,0.10),
circle(5,-8,0.08),circle(5,-8,0.10),
circle(6,-5,0.08),circle(6,-5,0.10),
circle(7,0,0.08),circle(7,0,0.10),
circle(8,7,0.08),circle(8,7,0.10)

)}}}


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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=x^2-8x+7}}}:



{{{ drawing(500, 500,-10,10,-10,10,
grid(1),
graph(500, 500,-10,10,-10,10, x^2-8x+7),
circle(0,7,0.08),circle(0,7,0.10),
circle(1,0,0.08),circle(1,0,0.10),
circle(2,-5,0.08),circle(2,-5,0.10),
circle(3,-8,0.08),circle(3,-8,0.10),
circle(4,-9,0.08),circle(4,-9,0.10),
circle(5,-8,0.08),circle(5,-8,0.10),
circle(6,-5,0.08),circle(6,-5,0.10),
circle(7,0,0.08),circle(7,0,0.10),
circle(8,7,0.08),circle(8,7,0.10)

)}}} Graph of {{{y=x^2-8x+7}}}