Question 125371


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


We can start at any x value, so lets start at x=-1





Lets evaluate {{{f(-1)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(-1)=(-1)^2-4(-1)}}} Plug in {{{x=-1}}}



{{{f(-1)=(1)-4(-1)}}} Evaluate {{{(-1)^2}}} to get 1

 

{{{f(-1)=1+4}}} Multiply -4 and  -1  to get 4

  

{{{f(-1)=5}}} Now combine like terms



So when {{{x=-1}}}, {{{f(x)=5}}}




-------Now lets find another point-------




Lets evaluate {{{f(0)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(0)=(0)^2-4(0)}}} Plug in {{{x=0}}}



{{{f(0)=(0)-4(0)}}} Evaluate {{{1(0)^2}}} to get 10

 

{{{f(0)=00}}} Multiply -4 and  0  to get 0

  

{{{f(0)=0}}} Now combine like terms



So when {{{x=0}}}, {{{f(x)=0}}}




-------Now lets find another point-------




Lets evaluate {{{f(1)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(1)=(1)^2-4(1)}}} Plug in {{{x=1}}}



{{{f(1)=(1)-4(1)}}} Evaluate {{{1(1)^2}}} to get 11

 

{{{f(1)=1-4}}} Multiply -4 and  1  to get -4

  

{{{f(1)=-3}}} Now combine like terms



So when {{{x=1}}}, {{{f(x)=-3}}}




-------Now lets find another point-------




Lets evaluate {{{f(2)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(2)=(2)^2-4(2)}}} Plug in {{{x=2}}}



{{{f(2)=(4)-4(2)}}} Evaluate {{{1(2)^2}}} to get 14

 

{{{f(2)=4-8}}} Multiply -4 and  2  to get -8

  

{{{f(2)=-4}}} Now combine like terms



So when {{{x=2}}}, {{{f(x)=-4}}}




-------Now lets find another point-------




Lets evaluate {{{f(3)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(3)=(3)^2-4(3)}}} Plug in {{{x=3}}}



{{{f(3)=(9)-4(3)}}} Evaluate {{{1(3)^2}}} to get 19

 

{{{f(3)=9-12}}} Multiply -4 and  3  to get -12

  

{{{f(3)=-3}}} Now combine like terms



So when {{{x=3}}}, {{{f(x)=-3}}}




-------Now lets find another point-------




Lets evaluate {{{f(4)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(4)=(4)^2-4(4)}}} Plug in {{{x=4}}}



{{{f(4)=(16)-4(4)}}} Evaluate {{{1(4)^2}}} to get 116

 

{{{f(4)=16-16}}} Multiply -4 and  4  to get -16

  

{{{f(4)=0}}} Now combine like terms



So when {{{x=4}}}, {{{f(x)=0}}}




-------Now lets find another point-------




Lets evaluate {{{f(5)}}}


{{{f(x)=x^2-4x}}} Start with the given polynomial



{{{f(5)=(5)^2-4(5)}}} Plug in {{{x=5}}}



{{{f(5)=(25)-4(5)}}} Evaluate {{{1(5)^2}}} to get 125

 

{{{f(5)=25-20}}} Multiply -4 and  5  to get -20

  

{{{f(5)=5}}} Now combine like terms



So when {{{x=5}}}, {{{f(x)=5}}}



Now lets make a table of the values we have calculated

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>

<TR><TD> -1</TD><TD>5</TD></TR> 
<TR><TD> 0</TD><TD>0</TD></TR> 
<TR><TD> 1</TD><TD>-3</TD></TR> 
<TR><TD> 2</TD><TD>-4</TD></TR> 
<TR><TD> 3</TD><TD>-3</TD></TR> 
<TR><TD> 4</TD><TD>0</TD></TR> 
<TR><TD> 5</TD><TD>5</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-10,10,-10,10,
  grid( 1 ),
circle(-1,5,0.05),
circle(-1,5,0.08),
circle(0,0,0.05),
circle(0,0,0.08),
circle(1,-3,0.05),
circle(1,-3,0.08),
circle(2,-4,0.05),
circle(2,-4,0.08),
circle(3,-3,0.05),
circle(3,-3,0.08),
circle(4,0,0.05),
circle(4,0,0.08),
circle(5,5,0.05),
circle(5,5,0.08))}}}



Now connect the points to graph {{{y=x^2-4x}}}  (note: the more points you plot, the easier it is to draw the graph)

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, x^2-4x),
circle(-1,5,0.05),
circle(-1,5,0.08),
circle(0,0,0.05),
circle(0,0,0.08),
circle(1,-3,0.05),
circle(1,-3,0.08),
circle(2,-4,0.05),
circle(2,-4,0.08),
circle(3,-3,0.05),
circle(3,-3,0.08),
circle(4,0,0.05),
circle(4,0,0.08),
circle(5,5,0.05),
circle(5,5,0.08))}}}