Question 128612
In order to generate ordered pairs, we need to plot evaluate some x values to get some y values to get the points.



So let's find the first point:




{{{f(x)=1x^2-3}}} Start with the given function



{{{f(-5)=1(-5)^2-3}}} Plug in {{{x=-5}}}



{{{f(-5)=1*25-3}}} Raise -5 to the 2nd power to get 25



{{{f(-5)=25-3}}} Multiply 1 and 25 to get 25



{{{f(-5)=22}}} Subtract 3 from 25 to get 22



So when {{{x=-5}}}, we have {{{y=22}}}



So our 1st point is (-5,22)



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



{{{f(x)=1x^2-3}}} Start with the given function



{{{f(-4)=1(-4)^2-3}}} Plug in {{{x=-4}}}



{{{f(-4)=1*16-3}}} Raise -4 to the 2nd power to get 16



{{{f(-4)=16-3}}} Multiply 1 and 16 to get 16



{{{f(-4)=13}}} Subtract 3 from 16 to get 13



So when {{{x=-4}}}, we have {{{y=13}}}



So our 2nd point is (-4,13)



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



{{{f(x)=1x^2-3}}} Start with the given function



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



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



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



{{{f(-3)=6}}} Subtract 3 from 9 to get 6



So when {{{x=-3}}}, we have {{{y=6}}}



So our 3rd point is (-3,6)



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



{{{f(x)=1x^2-3}}} Start with the given function



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



{{{f(-2)=1*4-3}}} Raise -2 to the 2nd power to get 4



{{{f(-2)=4-3}}} Multiply 1 and 4 to get 4



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



So when {{{x=-2}}}, we have {{{y=1}}}



So our 4th point is (-2,1)



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



{{{f(x)=1x^2-3}}} Start with the given function



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



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



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



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



So when {{{x=-1}}}, we have {{{y=-2}}}



So our 5th point is (-1,-2)



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



{{{f(x)=1x^2-3}}} Start with the given function



{{{f(0)=1(0)^2-3}}} Plug in {{{x=0}}}



{{{f(0)=1*0-3}}} Raise 0 to the 2nd power to get 0



{{{f(0)=0-3}}} Multiply 1 and 0 to get 0



{{{f(0)=-3}}} Subtract 3 from 0 to get -3



So when {{{x=0}}}, we have {{{y=-3}}}



So our 6th point is (0,-3)



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



{{{f(x)=1x^2-3}}} Start with the given function



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



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



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



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



So when {{{x=1}}}, we have {{{y=-2}}}



So our 7th point is (1,-2)



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



{{{f(x)=1x^2-3}}} Start with the given function



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



{{{f(2)=1*4-3}}} Raise 2 to the 2nd power to get 4



{{{f(2)=4-3}}} Multiply 1 and 4 to get 4



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



So when {{{x=2}}}, we have {{{y=1}}}



So our 8th point is (2,1)



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



{{{f(x)=1x^2-3}}} Start with the given function



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



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



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



{{{f(3)=6}}} Subtract 3 from 9 to get 6



So when {{{x=3}}}, we have {{{y=6}}}



So our 9th point is (3,6)



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



{{{f(x)=1x^2-3}}} Start with the given function



{{{f(4)=1(4)^2-3}}} Plug in {{{x=4}}}



{{{f(4)=1*16-3}}} Raise 4 to the 2nd power to get 16



{{{f(4)=16-3}}} Multiply 1 and 16 to get 16



{{{f(4)=13}}} Subtract 3 from 16 to get 13



So when {{{x=4}}}, we have {{{y=13}}}



So our 10th point is (4,13)



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



{{{f(x)=1x^2-3}}} Start with the given function



{{{f(5)=1(5)^2-3}}} Plug in {{{x=5}}}



{{{f(5)=1*25-3}}} Raise 5 to the 2nd power to get 25



{{{f(5)=25-3}}} Multiply 1 and 25 to get 25



{{{f(5)=22}}} Subtract 3 from 25 to get 22



So when {{{x=5}}}, we have {{{y=22}}}



So our 11th point is (5,22)



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> -5</TD><TD>22</TD></TR> 
<TR><TD> -4</TD><TD>13</TD></TR> 
<TR><TD> -3</TD><TD>6</TD></TR> 
<TR><TD> -2</TD><TD>1</TD></TR> 
<TR><TD> -1</TD><TD>-2</TD></TR> 
<TR><TD> 0</TD><TD>-3</TD></TR> 
<TR><TD> 1</TD><TD>-2</TD></TR> 
<TR><TD> 2</TD><TD>1</TD></TR> 
<TR><TD> 3</TD><TD>6</TD></TR> 
<TR><TD> 4</TD><TD>13</TD></TR> 
<TR><TD> 5</TD><TD>22</TD></TR> 
</TABLE>
</pre>

Now plot the points. Note: you need to use Firefox to see the next two graphs.

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
circle(-5,22,0.05),
circle(-5,22,0.08),
circle(-5,22,0.05),
circle(-5,22,0.1),
circle(-5,22,0.05),
circle(-5,22,0.12),
circle(-4,13,0.05),
circle(-4,13,0.08),
circle(-4,13,0.05),
circle(-4,13,0.1),
circle(-4,13,0.05),
circle(-4,13,0.12),
circle(-3,6,0.05),
circle(-3,6,0.08),
circle(-3,6,0.05),
circle(-3,6,0.1),
circle(-3,6,0.05),
circle(-3,6,0.12),
circle(-2,1,0.05),
circle(-2,1,0.08),
circle(-2,1,0.05),
circle(-2,1,0.1),
circle(-2,1,0.05),
circle(-2,1,0.12),
circle(-1,-2,0.05),
circle(-1,-2,0.08),
circle(-1,-2,0.05),
circle(-1,-2,0.1),
circle(-1,-2,0.05),
circle(-1,-2,0.12),
circle(0,-3,0.05),
circle(0,-3,0.08),
circle(0,-3,0.05),
circle(0,-3,0.1),
circle(0,-3,0.05),
circle(0,-3,0.12),
circle(1,-2,0.05),
circle(1,-2,0.08),
circle(1,-2,0.05),
circle(1,-2,0.1),
circle(1,-2,0.05),
circle(1,-2,0.12),
circle(2,1,0.05),
circle(2,1,0.08),
circle(2,1,0.05),
circle(2,1,0.1),
circle(2,1,0.05),
circle(2,1,0.12),
circle(3,6,0.05),
circle(3,6,0.08),
circle(3,6,0.05),
circle(3,6,0.1),
circle(3,6,0.05),
circle(3,6,0.12),
circle(4,13,0.05),
circle(4,13,0.08),
circle(4,13,0.05),
circle(4,13,0.1),
circle(4,13,0.05),
circle(4,13,0.12),
circle(5,22,0.05),
circle(5,22,0.08),
circle(5,22,0.05),
circle(5,22,0.1),
circle(5,22,0.05),
circle(5,22,0.12)
)}}}



Now connect the points to graph {{{y=1x^2-3}}}  (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^2-3),
circle(-5,22,0.05),
circle(-5,22,0.08),
circle(-5,22,0.05),
circle(-5,22,0.1),
circle(-5,22,0.05),
circle(-5,22,0.12),
circle(-4,13,0.05),
circle(-4,13,0.08),
circle(-4,13,0.05),
circle(-4,13,0.1),
circle(-4,13,0.05),
circle(-4,13,0.12),
circle(-3,6,0.05),
circle(-3,6,0.08),
circle(-3,6,0.05),
circle(-3,6,0.1),
circle(-3,6,0.05),
circle(-3,6,0.12),
circle(-2,1,0.05),
circle(-2,1,0.08),
circle(-2,1,0.05),
circle(-2,1,0.1),
circle(-2,1,0.05),
circle(-2,1,0.12),
circle(-1,-2,0.05),
circle(-1,-2,0.08),
circle(-1,-2,0.05),
circle(-1,-2,0.1),
circle(-1,-2,0.05),
circle(-1,-2,0.12),
circle(0,-3,0.05),
circle(0,-3,0.08),
circle(0,-3,0.05),
circle(0,-3,0.1),
circle(0,-3,0.05),
circle(0,-3,0.12),
circle(1,-2,0.05),
circle(1,-2,0.08),
circle(1,-2,0.05),
circle(1,-2,0.1),
circle(1,-2,0.05),
circle(1,-2,0.12),
circle(2,1,0.05),
circle(2,1,0.08),
circle(2,1,0.05),
circle(2,1,0.1),
circle(2,1,0.05),
circle(2,1,0.12),
circle(3,6,0.05),
circle(3,6,0.08),
circle(3,6,0.05),
circle(3,6,0.1),
circle(3,6,0.05),
circle(3,6,0.12),
circle(4,13,0.05),
circle(4,13,0.08),
circle(4,13,0.05),
circle(4,13,0.1),
circle(4,13,0.05),
circle(4,13,0.12),
circle(5,22,0.05),
circle(5,22,0.08),
circle(5,22,0.05),
circle(5,22,0.1),
circle(5,22,0.05),
circle(5,22,0.12)
)}}}