Question 87018
In order to graph {{{y=-x^2+2}}}, we need to plot some points.
We can start at any x value, so lets start at x=-3


{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(-3)=-7}}} Evaluate the expression by following the order of operations


So our first point is (-3,-7)





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




{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(-2)=-2}}} Evaluate the expression by following the order of operations


So our second point is (-2,-2)





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




{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(-1)=1}}} Evaluate the expression by following the order of operations


So our third point is (-1,1)





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




{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(0)=2}}} Evaluate the expression by following the order of operations


So our fourth point is (0,2)





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




{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(1)=1}}} Evaluate the expression by following the order of operations


So our fifth point is (1,1)





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




{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(2)=-2}}} Evaluate the expression by following the order of operations


So our sixth point is (2,-2)





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




{{{h(x)=-x^2+2}}} Start with the given polynomial 

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


{{{h(3)=-7}}} Evaluate the expression by following the order of operations


So our seventh point is (3,-7)





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




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>-7</TD></TR> 
<TR><TD> -2</TD><TD>-2</TD></TR> 
<TR><TD> -1</TD><TD>1</TD></TR> 
<TR><TD> 0</TD><TD>2</TD></TR> 
<TR><TD> 1</TD><TD>1</TD></TR> 
<TR><TD> 2</TD><TD>-2</TD></TR> 
<TR><TD> 3</TD><TD>-7</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-10,10,-10,10,
  grid( 1 ),circle(-3,-7,0.05),
circle(-3,-7,0.08),
circle(-2,-2,0.05),
circle(-2,-2,0.08),
circle(-1,1,0.05),
circle(-1,1,0.08),
circle(0,2,0.05),
circle(0,2,0.08),
circle(1,1,0.05),
circle(1,1,0.08),
circle(2,-2,0.05),
circle(2,-2,0.08),
circle(3,-7,0.05),
circle(3,-7,0.08))}}}



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

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, -x^2+2),circle(-3,-7,0.05),
circle(-3,-7,0.08),
circle(-2,-2,0.05),
circle(-2,-2,0.08),
circle(-1,1,0.05),
circle(-1,1,0.08),
circle(0,2,0.05),
circle(0,2,0.08),
circle(1,1,0.05),
circle(1,1,0.08),
circle(2,-2,0.05),
circle(2,-2,0.08),
circle(3,-7,0.05),
circle(3,-7,0.08))}}}