Question 88244


In order to graph {{{y=-x^2+x}}}, we need to plot some points.
We can start at any x value, so lets start at x=-3




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(9)+(-3)}}} Raise -3 to the second power to get 9



{{{y=-12}}} Now combine like terms


So our 1st point is (-3,-12)




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




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(4)+(-2)}}} Raise -2 to the second power to get 4



{{{y=-6}}} Now combine like terms


So our 2nd point is (-2,-6)




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




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(1)+(-1)}}} Raise -1 to the second power to get 1



{{{y=-2}}} Now combine like terms


So our 3rd point is (-1,-2)




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




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(0)+(0)}}} Raise 0 to the second power to get 0



{{{y=0}}} Now combine like terms


So our 4th point is (0,0)




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




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(1)+(1)}}} Raise 1 to the second power to get 1



{{{y=0}}} Now combine like terms


So our 5th point is (1,0)




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




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(4)+(2)}}} Raise 2 to the second power to get 4



{{{y=-2}}} Now combine like terms


So our 6th point is (2,-2)




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




{{{y=-x^2+x}}} Start with the given polynomial



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



{{{y=-(9)+(3)}}} Raise 3 to the second power to get 9



{{{y=-6}}} Now combine like terms


So our 7th point is (3,-6)



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> -3</TD><TD>-12</TD></TR> 
<TR><TD> -2</TD><TD>-6</TD></TR> 
<TR><TD> -1</TD><TD>-2</TD></TR> 
<TR><TD> 0</TD><TD>0</TD></TR> 
<TR><TD> 1</TD><TD>0</TD></TR> 
<TR><TD> 2</TD><TD>-2</TD></TR> 
<TR><TD> 3</TD><TD>-6</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-10,10,-10,10,
  grid( 1 ),circle(-3,-12,0.05),
circle(-3,-12,0.08),
circle(-2,-6,0.05),
circle(-2,-6,0.08),
circle(-1,-2,0.05),
circle(-1,-2,0.08),
circle(0,0,0.05),
circle(0,0,0.08),
circle(1,0,0.05),
circle(1,0,0.08),
circle(2,-2,0.05),
circle(2,-2,0.08),
circle(3,-6,0.05),
circle(3,-6,0.08))}}}



Now connect the points to graph {{{y=-x^2+x}}}

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, -x^2+x),circle(-3,-12,0.05),
circle(-3,-12,0.08),
circle(-2,-6,0.05),
circle(-2,-6,0.08),
circle(-1,-2,0.05),
circle(-1,-2,0.08),
circle(0,0,0.05),
circle(0,0,0.08),
circle(1,0,0.05),
circle(1,0,0.08),
circle(2,-2,0.05),
circle(2,-2,0.08),
circle(3,-6,0.05),
circle(3,-6,0.08))}}}