Question 85545
{{{y=x^2+2}}} Start with the given equation

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

{{{y=1(4)+2}}} Square -2

{{{y=4+2}}} Multiply

{{{y=6}}} Add



So we have the point (-2,6)


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

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

{{{y=1(1)+2}}} Square -1

{{{y=1+2}}} Multiply

{{{y=3}}} Add



So we have the point (-1,3)


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

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

{{{y=1(0)+2}}} Square 0

{{{y=0+2}}} Multiply

{{{y=2}}} Add



So we have the point (0,2)


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

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

{{{y=1(1)+2}}} Square 1

{{{y=1+2}}} Multiply

{{{y=3}}} Add



So we have the point (1,3)


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

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

{{{y=1(4)+2}}} Square 2

{{{y=4+2}}} Multiply

{{{y=6}}} Add



So we have the point (2,6)


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

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

Now connect the points, this is the graph of {{{y=x^2+2}}}

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