Question 88249


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




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



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



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



{{{y=-(4)+-4}}} Multiply 2 by -2 to get -4



{{{y=-8}}} Now combine like terms


So our 1st point is (-2,-8)




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




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



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



{{{y=-(1)+2(-1)}}} Raise -1 to the second power to get 1



{{{y=-(1)+-2}}} Multiply 2 by -1 to get -2



{{{y=-3}}} Now combine like terms


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




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




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



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



{{{y=-(0)+2(0)}}} Raise 0 to the second power to get 0



{{{y=-(0)+0}}} Multiply 2 by 0 to get 0



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


So our 3rd point is (0,0)




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




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



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



{{{y=-(1)+2(1)}}} Raise 1 to the second power to get 1



{{{y=-(1)+2}}} Multiply 2 by 1 to get 2



{{{y=1}}} Now combine like terms


So our 4th point is (1,1)




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




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



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



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



{{{y=-(4)+4}}} Multiply 2 by 2 to get 4



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


So our 5th point is (2,0)




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




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



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



{{{y=-(9)+2(3)}}} Raise 3 to the second power to get 9



{{{y=-(9)+6}}} Multiply 2 by 3 to get 6



{{{y=-3}}} Now combine like terms


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




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




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



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



{{{y=-(16)+2(4)}}} Raise 4 to the second power to get 16



{{{y=-(16)+8}}} Multiply 2 by 4 to get 8



{{{y=-8}}} Now combine like terms


So our 7th point is (4,-8)



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> -2</TD><TD>-8</TD></TR> 
<TR><TD> -1</TD><TD>-3</TD></TR> 
<TR><TD> 0</TD><TD>0</TD></TR> 
<TR><TD> 1</TD><TD>1</TD></TR> 
<TR><TD> 2</TD><TD>0</TD></TR> 
<TR><TD> 3</TD><TD>-3</TD></TR> 
<TR><TD> 4</TD><TD>-8</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-10,10,-10,10,
  grid( 1 ),circle(-2,-8,0.05),
circle(-2,-8,0.08),
circle(-1,-3,0.05),
circle(-1,-3,0.08),
circle(0,0,0.05),
circle(0,0,0.08),
circle(1,1,0.05),
circle(1,1,0.08),
circle(2,0,0.05),
circle(2,0,0.08),
circle(3,-3,0.05),
circle(3,-3,0.08),
circle(4,-8,0.05),
circle(4,-8,0.08))}}}



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

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, -x^2+2x),circle(-2,-8,0.05),
circle(-2,-8,0.08),
circle(-1,-3,0.05),
circle(-1,-3,0.08),
circle(0,0,0.05),
circle(0,0,0.08),
circle(1,1,0.05),
circle(1,1,0.08),
circle(2,0,0.05),
circle(2,0,0.08),
circle(3,-3,0.05),
circle(3,-3,0.08),
circle(4,-8,0.05),
circle(4,-8,0.08))}}}