Question 127270
In order to graph {{{f(x)=1x^2-1}}}, 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^2-1}}} Start with the given function



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



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



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



{{{f(-2)=3}}} Subtract 1 from 4 to get 3



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



So our 1st point is (-2,3)



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



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



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



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



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



{{{f(-1)=0}}} Subtract 1 from 1 to get 0



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



So our 2nd point is (-1,0)



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



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



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



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



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



{{{f(0)=-1}}} Subtract 1 from 0 to get -1



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



So our 3rd point is (0,-1)



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



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



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



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



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



{{{f(1)=0}}} Subtract 1 from 1 to get 0



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



So our 4th point is (1,0)



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



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



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



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



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



{{{f(2)=3}}} Subtract 1 from 4 to get 3



So when {{{x=2}}}, we have {{{y=3}}}



So our 5th point is (2,3)



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,-15,15,-15,15,
  grid( 1 ),
circle(-2,3,0.05),
circle(-2,3,0.08),
circle(-2,3,0.05),
circle(-2,3,0.1),
circle(-2,3,0.05),
circle(-2,3,0.12),
circle(-1,0,0.05),
circle(-1,0,0.08),
circle(-1,0,0.05),
circle(-1,0,0.1),
circle(-1,0,0.05),
circle(-1,0,0.12),
circle(0,-1,0.05),
circle(0,-1,0.08),
circle(0,-1,0.05),
circle(0,-1,0.1),
circle(0,-1,0.05),
circle(0,-1,0.12),
circle(1,0,0.05),
circle(1,0,0.08),
circle(1,0,0.05),
circle(1,0,0.1),
circle(1,0,0.05),
circle(1,0,0.12),
circle(2,3,0.05),
circle(2,3,0.08),
circle(2,3,0.05),
circle(2,3,0.1),
circle(2,3,0.05),
circle(2,3,0.12)
)}}}



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