Question 131616
Do you want to graph?


In order to graph {{{f(x)=1x^2+2}}}, we need to plot some points. To do that, we need to plug in some x values to get some y values



So let's find the first point:




{{{f(x)=1x^2+2}}} Start with the given function



{{{f(-3)=1(-3)^2+2}}} Plug in {{{x=-3}}}



{{{f(-3)=1*9+2}}} Raise -3 to the 2nd power to get 9



{{{f(-3)=9+2}}} Multiply 1 and 9 to get 9



{{{f(-3)=11}}} Add 9 and 2 to get 11



So when {{{x=-3}}}, we have {{{y=11}}}



So our 1st point is (-3,11)



--------------  Let's find another point  --------------



{{{f(x)=1x^2+2}}} Start with the given function



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



{{{f(-2)=1*4+2}}} Raise -2 to the 2nd power to get 4



{{{f(-2)=4+2}}} Multiply 1 and 4 to get 4



{{{f(-2)=6}}} Add 4 and 2 to get 6



So when {{{x=-2}}}, we have {{{y=6}}}



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



--------------  Let's find another point  --------------



{{{f(x)=1x^2+2}}} Start with the given function



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



{{{f(-1)=1*1+2}}} Raise -1 to the 2nd power to get 1



{{{f(-1)=1+2}}} Multiply 1 and 1 to get 1



{{{f(-1)=3}}} Add 1 and 2 to get 3



So when {{{x=-1}}}, we have {{{y=3}}}



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



--------------  Let's find another point  --------------



{{{f(x)=1x^2+2}}} Start with the given function



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



{{{f(0)=1*0+2}}} Raise 0 to the 2nd power to get 0



{{{f(0)=0+2}}} Multiply 1 and 0 to get 0



{{{f(0)=2}}} Add 0 and 2 to get 2



So when {{{x=0}}}, we have {{{y=2}}}



So our 4th point is (0,2)



--------------  Let's find another point  --------------



{{{f(x)=1x^2+2}}} Start with the given function



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



{{{f(1)=1*1+2}}} Raise 1 to the 2nd power to get 1



{{{f(1)=1+2}}} Multiply 1 and 1 to get 1



{{{f(1)=3}}} Add 1 and 2 to get 3



So when {{{x=1}}}, we have {{{y=3}}}



So our 5th point is (1,3)



--------------  Let's find another point  --------------



{{{f(x)=1x^2+2}}} Start with the given function



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



{{{f(2)=1*4+2}}} Raise 2 to the 2nd power to get 4



{{{f(2)=4+2}}} Multiply 1 and 4 to get 4



{{{f(2)=6}}} Add 4 and 2 to get 6



So when {{{x=2}}}, we have {{{y=6}}}



So our 6th point is (2,6)



--------------  Let's find another point  --------------



{{{f(x)=1x^2+2}}} Start with the given function



{{{f(3)=1(3)^2+2}}} Plug in {{{x=3}}}



{{{f(3)=1*9+2}}} Raise 3 to the 2nd power to get 9



{{{f(3)=9+2}}} Multiply 1 and 9 to get 9



{{{f(3)=11}}} Add 9 and 2 to get 11



So when {{{x=3}}}, we have {{{y=11}}}



So our 7th point is (3,11)



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>11</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> 
<TR><TD> 3</TD><TD>11</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
circle(-3,11,0.05),
circle(-3,11,0.08),
circle(-3,11,0.05),
circle(-3,11,0.1),
circle(-3,11,0.05),
circle(-3,11,0.12),
circle(-2,6,0.05),
circle(-2,6,0.08),
circle(-2,6,0.05),
circle(-2,6,0.1),
circle(-2,6,0.05),
circle(-2,6,0.12),
circle(-1,3,0.05),
circle(-1,3,0.08),
circle(-1,3,0.05),
circle(-1,3,0.1),
circle(-1,3,0.05),
circle(-1,3,0.12),
circle(0,2,0.05),
circle(0,2,0.08),
circle(0,2,0.05),
circle(0,2,0.1),
circle(0,2,0.05),
circle(0,2,0.12),
circle(1,3,0.05),
circle(1,3,0.08),
circle(1,3,0.05),
circle(1,3,0.1),
circle(1,3,0.05),
circle(1,3,0.12),
circle(2,6,0.05),
circle(2,6,0.08),
circle(2,6,0.05),
circle(2,6,0.1),
circle(2,6,0.05),
circle(2,6,0.12),
circle(3,11,0.05),
circle(3,11,0.08),
circle(3,11,0.05),
circle(3,11,0.1),
circle(3,11,0.05),
circle(3,11,0.12)
)}}}



Now connect the points to graph {{{y=1x^2+2}}}  (note: the more points you plot, the easier it is to draw the graph)

{{{drawing(900,900,-15,15,-15,15,
grid( 1 ),
graph(900,900,-15,15,-15,15, 1x^2+2),
circle(-3,11,0.05),
circle(-3,11,0.08),
circle(-3,11,0.05),
circle(-3,11,0.1),
circle(-3,11,0.05),
circle(-3,11,0.12),
circle(-2,6,0.05),
circle(-2,6,0.08),
circle(-2,6,0.05),
circle(-2,6,0.1),
circle(-2,6,0.05),
circle(-2,6,0.12),
circle(-1,3,0.05),
circle(-1,3,0.08),
circle(-1,3,0.05),
circle(-1,3,0.1),
circle(-1,3,0.05),
circle(-1,3,0.12),
circle(0,2,0.05),
circle(0,2,0.08),
circle(0,2,0.05),
circle(0,2,0.1),
circle(0,2,0.05),
circle(0,2,0.12),
circle(1,3,0.05),
circle(1,3,0.08),
circle(1,3,0.05),
circle(1,3,0.1),
circle(1,3,0.05),
circle(1,3,0.12),
circle(2,6,0.05),
circle(2,6,0.08),
circle(2,6,0.05),
circle(2,6,0.1),
circle(2,6,0.05),
circle(2,6,0.12),
circle(3,11,0.05),
circle(3,11,0.08),
circle(3,11,0.05),
circle(3,11,0.1),
circle(3,11,0.05),
circle(3,11,0.12)
)}}}