Question 130545
In order to graph {{{f(x)=1x^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}}} Start with the given function



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



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



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



So when {{{x=-3}}}, we have {{{y=9}}}



So our 1st point is (-3,9)



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



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



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



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



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



So when {{{x=-2}}}, we have {{{y=4}}}



So our 2nd point is (-2,4)



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



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



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



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



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



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



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



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



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



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



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



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



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



So our 4th point is (0,0)



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



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



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



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



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



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



So our 5th point is (1,1)



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



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



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



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



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



So when {{{x=2}}}, we have {{{y=4}}}



So our 6th point is (2,4)



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



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



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



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



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



So when {{{x=3}}}, we have {{{y=9}}}



So our 7th point is (3,9)



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>9</TD></TR> 
<TR><TD> -2</TD><TD>4</TD></TR> 
<TR><TD> -1</TD><TD>1</TD></TR> 
<TR><TD> 0</TD><TD>0</TD></TR> 
<TR><TD> 1</TD><TD>1</TD></TR> 
<TR><TD> 2</TD><TD>4</TD></TR> 
<TR><TD> 3</TD><TD>9</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
circle(-3,9,0.05),
circle(-3,9,0.08),
circle(-3,9,0.05),
circle(-3,9,0.1),
circle(-3,9,0.05),
circle(-3,9,0.12),
circle(-2,4,0.05),
circle(-2,4,0.08),
circle(-2,4,0.05),
circle(-2,4,0.1),
circle(-2,4,0.05),
circle(-2,4,0.12),
circle(-1,1,0.05),
circle(-1,1,0.08),
circle(-1,1,0.05),
circle(-1,1,0.1),
circle(-1,1,0.05),
circle(-1,1,0.12),
circle(0,0,0.05),
circle(0,0,0.08),
circle(0,0,0.05),
circle(0,0,0.1),
circle(0,0,0.05),
circle(0,0,0.12),
circle(1,1,0.05),
circle(1,1,0.08),
circle(1,1,0.05),
circle(1,1,0.1),
circle(1,1,0.05),
circle(1,1,0.12),
circle(2,4,0.05),
circle(2,4,0.08),
circle(2,4,0.05),
circle(2,4,0.1),
circle(2,4,0.05),
circle(2,4,0.12),
circle(3,9,0.05),
circle(3,9,0.08),
circle(3,9,0.05),
circle(3,9,0.1),
circle(3,9,0.05),
circle(3,9,0.12)
)}}}



Now connect the points to graph {{{y=1x^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),
circle(-3,9,0.05),
circle(-3,9,0.08),
circle(-3,9,0.05),
circle(-3,9,0.1),
circle(-3,9,0.05),
circle(-3,9,0.12),
circle(-2,4,0.05),
circle(-2,4,0.08),
circle(-2,4,0.05),
circle(-2,4,0.1),
circle(-2,4,0.05),
circle(-2,4,0.12),
circle(-1,1,0.05),
circle(-1,1,0.08),
circle(-1,1,0.05),
circle(-1,1,0.1),
circle(-1,1,0.05),
circle(-1,1,0.12),
circle(0,0,0.05),
circle(0,0,0.08),
circle(0,0,0.05),
circle(0,0,0.1),
circle(0,0,0.05),
circle(0,0,0.12),
circle(1,1,0.05),
circle(1,1,0.08),
circle(1,1,0.05),
circle(1,1,0.1),
circle(1,1,0.05),
circle(1,1,0.12),
circle(2,4,0.05),
circle(2,4,0.08),
circle(2,4,0.05),
circle(2,4,0.1),
circle(2,4,0.05),
circle(2,4,0.12),
circle(3,9,0.05),
circle(3,9,0.08),
circle(3,9,0.05),
circle(3,9,0.1),
circle(3,9,0.05),
circle(3,9,0.12)
)}}}