Question 93226


In order to graph {{{y=-x^2+1}}}, we need to plot some points.


We can start at any x value, so lets start at x=-2





Lets find the value of y when  {{{x=-2}}}


{{{y=-x^2+1}}} Start with the given polynomial



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



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

 

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

  

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



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




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




Lets find the value of y when  {{{x=-1}}}


{{{y=-x^2+1}}} Start with the given polynomial



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



{{{y=-1+1}}} Evaluate {{{(-1)^2}}} to get 1

 

{{{y=-1+1}}} Multiply -1 and  1  to get -1

  

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



So when {{{x=-1}}}, {{{y=0}}}




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




Lets find the value of y when  {{{x=0}}}


{{{y=-x^2+1}}} Start with the given polynomial



{{{y=-(0)^2+1}}} Plug in {{{x=0}}}



{{{y=-0+1}}} Evaluate {{{(0)^2}}} to get 0

 

{{{y=0+1}}} Multiply -1 and  0  to get 0

  

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



So when {{{x=0}}}, {{{y=1}}}




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




Lets find the value of y when  {{{x=1}}}


{{{y=-x^2+1}}} Start with the given polynomial



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



{{{y=-1+1}}} Evaluate {{{(1)^2}}} to get 1

 

{{{y=-1+1}}} Multiply -1 and  1  to get -1

  

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



So when {{{x=1}}}, {{{y=0}}}




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




Lets find the value of y when  {{{x=2}}}


{{{y=-x^2+1}}} Start with the given polynomial



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



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

 

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

  

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



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



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

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



Now connect the points to graph {{{y=-x^2+1}}}  (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+1),
circle(-2,-3,0.05),
circle(-2,-3,0.08),
circle(-1,0,0.05),
circle(-1,0,0.08),
circle(0,1,0.05),
circle(0,1,0.08),
circle(1,0,0.05),
circle(1,0,0.08),
circle(2,-3,0.05),
circle(2,-3,0.08))}}}