Question 173971
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In order to graph {{{y=x^2-5x+4}}}, we need to plot some points.



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

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



{{{y=x^2-5x+4}}} Start with the given equation.



{{{y=(0)^2-5(0)+4}}} Plug in {{{x=0}}}.



{{{y=1(0)-5(0)+4}}} Square {{{0}}} to get {{{0}}}.



{{{y=0-5(0)+4}}} Multiply {{{1}}} and {{{0}}} to get {{{0}}}.



{{{y=0+0+4}}} Multiply {{{-5}}} and {{{0}}} to get {{{0}}}.



{{{y=4}}} Combine like terms.



So when {{{x=0}}}, then {{{y=4}}}.



So we have the point *[Tex \LARGE \left(0,4\right)].



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



{{{y=x^2-5x+4}}} Start with the given equation.



{{{y=(1)^2-5(1)+4}}} Plug in {{{x=1}}}.



{{{y=1(1)-5(1)+4}}} Square {{{1}}} to get {{{1}}}.



{{{y=1-5(1)+4}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1-5+4}}} Multiply {{{-5}}} and {{{1}}} to get {{{-5}}}.



{{{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^2-5x+4}}} Start with the given equation.



{{{y=(2)^2-5(2)+4}}} Plug in {{{x=2}}}.



{{{y=1(4)-5(2)+4}}} Square {{{2}}} to get {{{4}}}.



{{{y=4-5(2)+4}}} Multiply {{{1}}} and {{{4}}} to get {{{4}}}.



{{{y=4-10+4}}} Multiply {{{-5}}} and {{{2}}} to get {{{-10}}}.



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



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



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



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



{{{y=x^2-5x+4}}} Start with the given equation.



{{{y=(3)^2-5(3)+4}}} Plug in {{{x=3}}}.



{{{y=1(9)-5(3)+4}}} Square {{{3}}} to get {{{9}}}.



{{{y=9-5(3)+4}}} Multiply {{{1}}} and {{{9}}} to get {{{9}}}.



{{{y=9-15+4}}} Multiply {{{-5}}} and {{{3}}} to get {{{-15}}}.



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



So when {{{x=3}}}, then {{{y=-2}}}.



So we have the point *[Tex \LARGE \left(3,-2\right)].



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



{{{y=x^2-5x+4}}} Start with the given equation.



{{{y=(4)^2-5(4)+4}}} Plug in {{{x=4}}}.



{{{y=1(16)-5(4)+4}}} Square {{{4}}} to get {{{16}}}.



{{{y=16-5(4)+4}}} Multiply {{{1}}} and {{{16}}} to get {{{16}}}.



{{{y=16-20+4}}} Multiply {{{-5}}} and {{{4}}} to get {{{-20}}}.



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



So when {{{x=4}}}, then {{{y=0}}}.



So we have the point *[Tex \LARGE \left(4,0\right)].



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



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



{{{y=x^2-5x+4}}} Start with the given equation.



{{{y=(5)^2-5(5)+4}}} Plug in {{{x=5}}}.



{{{y=1(25)-5(5)+4}}} Square {{{5}}} to get {{{25}}}.



{{{y=25-5(5)+4}}} Multiply {{{1}}} and {{{25}}} to get {{{25}}}.



{{{y=25-25+4}}} Multiply {{{-5}}} and {{{5}}} to get {{{-25}}}.



{{{y=4}}} Combine like terms.



So when {{{x=5}}}, then {{{y=4}}}.



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

)}}}


<a name="graph">



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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=x^2-5x+4}}}:



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

)}}} Graph of {{{y=x^2-5x+4}}}