Question 111767

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



{{{f(-2)=(-2)^2-1(-2)-2}}} Plug in {{{x=-2}}}. In other words, replace each x with -2.



{{{f(-2)=(4)-1(-2)-2}}} Evaluate {{{(-2)^2}}} to get 4.



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



{{{f(-2)=4}}} Now combine like terms



-----------Now let's evaluate another value---------



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



{{{f(-1)=(-1)^2-1(-1)-2}}} Plug in {{{x=-1}}}. In other words, replace each x with -1.



{{{f(-1)=(1)-1(-1)-2}}} Evaluate {{{(-1)^2}}} to get 1.



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



{{{f(-1)=0}}} Now combine like terms



-----------Now let's evaluate another value---------



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



{{{f(0)=(0)^2-1(0)-2}}} Plug in {{{x=0}}}. In other words, replace each x with 0.



{{{f(0)=(0)-1(0)-2}}} Evaluate {{{(0)^2}}} to get 0.



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



{{{f(0)=-2}}} Now combine like terms



-----------Now let's evaluate another value---------



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



{{{f(1)=(1)^2-1(1)-2}}} Plug in {{{x=1}}}. In other words, replace each x with 1.



{{{f(1)=(1)-1(1)-2}}} Evaluate {{{(1)^2}}} to get 1.



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



{{{f(1)=-2}}} Now combine like terms



-----------Now let's evaluate another value---------



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



{{{f(2)=(2)^2-1(2)-2}}} Plug in {{{x=2}}}. In other words, replace each x with 2.



{{{f(2)=(4)-1(2)-2}}} Evaluate {{{(2)^2}}} to get 4.



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



{{{f(2)=0}}} Now combine like terms



-----------Now let's evaluate another value---------



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



{{{f(3)=(3)^2-1(3)-2}}} Plug in {{{x=3}}}. In other words, replace each x with 3.



{{{f(3)=(9)-1(3)-2}}} Evaluate {{{(3)^2}}} to get 9.



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



{{{f(3)=4}}} Now combine like terms





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

{{{drawing(900,900,-10,10,-10,10,
  grid( 1 ),
circle(-2,4,0.05),
circle(-2,4,0.08),
circle(-1,0,0.05),
circle(-1,0,0.08),
circle(0,-2,0.05),
circle(0,-2,0.08),
circle(1,-2,0.05),
circle(1,-2,0.08),
circle(2,0,0.05),
circle(2,0,0.08),
circle(3,4,0.05),
circle(3,4,0.08))}}}



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

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
graph(900,900,-10,10,-10,10, x^2-x-2),
circle(-2,4,0.05),
circle(-2,4,0.08),
circle(-1,0,0.05),
circle(-1,0,0.08),
circle(0,-2,0.05),
circle(0,-2,0.08),
circle(1,-2,0.05),
circle(1,-2,0.08),
circle(2,0,0.05),
circle(2,0,0.08),
circle(3,4,0.05),
circle(3,4,0.08))}}}