```Question 117549
In order to make a table, just plug in some n values. So I'm going to start at n=-5

Let's evaluate {{{f(-5)}}}

{{{f(-5)=2(-5)^2-4(-5)-6}}} Plug in {{{n=-5}}}. In other words, replace each n with -5.

{{{f(-5)=2(25)-4(-5)-6}}} Evaluate {{{(-5)^2}}} to get 25.

{{{f(-5)=+50-4(-5)-6}}} Multiply 2 and 25 to get  50

{{{f(-5)=+50+20-6}}} Multiply -4 and -5 to get  20

{{{f(-5)=64}}} Now combine like terms

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

Let's evaluate {{{f(-4)}}}

{{{f(-4)=2(-4)^2-4(-4)-6}}} Plug in {{{n=-4}}}. In other words, replace each n with -4.

{{{f(-4)=2(16)-4(-4)-6}}} Evaluate {{{(-4)^2}}} to get 16.

{{{f(-4)=+32-4(-4)-6}}} Multiply 2 and 16 to get  32

{{{f(-4)=+32+16-6}}} Multiply -4 and -4 to get  16

{{{f(-4)=42}}} Now combine like terms

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

Let's evaluate {{{f(-3)}}}

{{{f(-3)=2(-3)^2-4(-3)-6}}} Plug in {{{n=-3}}}. In other words, replace each n with -3.

{{{f(-3)=2(9)-4(-3)-6}}} Evaluate {{{(-3)^2}}} to get 9.

{{{f(-3)=+18-4(-3)-6}}} Multiply 2 and 9 to get  18

{{{f(-3)=+18+12-6}}} Multiply -4 and -3 to get  12

{{{f(-3)=24}}} Now combine like terms

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

Let's evaluate {{{f(-2)}}}

{{{f(-2)=2(-2)^2-4(-2)-6}}} Plug in {{{n=-2}}}. In other words, replace each n with -2.

{{{f(-2)=2(4)-4(-2)-6}}} Evaluate {{{(-2)^2}}} to get 4.

{{{f(-2)=+8-4(-2)-6}}} Multiply 2 and 4 to get  8

{{{f(-2)=+8+8-6}}} Multiply -4 and -2 to get  8

{{{f(-2)=10}}} Now combine like terms

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

Let's evaluate {{{f(-1)}}}

{{{f(-1)=2(-1)^2-4(-1)-6}}} Plug in {{{n=-1}}}. In other words, replace each n with -1.

{{{f(-1)=2(1)-4(-1)-6}}} Evaluate {{{(-1)^2}}} to get 1.

{{{f(-1)=+2-4(-1)-6}}} Multiply 2 and 1 to get  2

{{{f(-1)=+2+4-6}}} Multiply -4 and -1 to get  4

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

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

Let's evaluate {{{f(0)}}}

{{{f(0)=2(0)^2-4(0)-6}}} Plug in {{{n=0}}}. In other words, replace each n with 0.

{{{f(0)=2(0)-4(0)-6}}} Evaluate {{{(0)^2}}} to get 0.

{{{f(0)=+0-4(0)-6}}} Multiply 2 and 0 to get  0

{{{f(0)=+0+0-6}}} Multiply -4 and 0 to get  0

{{{f(0)=-6}}} Now combine like terms

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

Let's evaluate {{{f(1)}}}

{{{f(1)=2(1)^2-4(1)-6}}} Plug in {{{n=1}}}. In other words, replace each n with 1.

{{{f(1)=2(1)-4(1)-6}}} Evaluate {{{(1)^2}}} to get 1.

{{{f(1)=+2-4(1)-6}}} Multiply 2 and 1 to get  2

{{{f(1)=+2-4-6}}} Multiply -4 and 1 to get  -4

{{{f(1)=-8}}} Now combine like terms

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

Let's evaluate {{{f(2)}}}

{{{f(2)=2(2)^2-4(2)-6}}} Plug in {{{n=2}}}. In other words, replace each n with 2.

{{{f(2)=2(4)-4(2)-6}}} Evaluate {{{(2)^2}}} to get 4.

{{{f(2)=+8-4(2)-6}}} Multiply 2 and 4 to get  8

{{{f(2)=+8-8-6}}} Multiply -4 and 2 to get  -8

{{{f(2)=-6}}} Now combine like terms

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

Let's evaluate {{{f(3)}}}

{{{f(3)=2(3)^2-4(3)-6}}} Plug in {{{n=3}}}. In other words, replace each n with 3.

{{{f(3)=2(9)-4(3)-6}}} Evaluate {{{(3)^2}}} to get 9.

{{{f(3)=+18-4(3)-6}}} Multiply 2 and 9 to get  18

{{{f(3)=+18-12-6}}} Multiply -4 and 3 to get  -12

{{{f(3)=0}}} Now combine like terms

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

Let's evaluate {{{f(4)}}}

{{{f(4)=2(4)^2-4(4)-6}}} Plug in {{{n=4}}}. In other words, replace each n with 4.

{{{f(4)=2(16)-4(4)-6}}} Evaluate {{{(4)^2}}} to get 16.

{{{f(4)=+32-4(4)-6}}} Multiply 2 and 16 to get  32

{{{f(4)=+32-16-6}}} Multiply -4 and 4 to get  -16

{{{f(4)=10}}} Now combine like terms

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

Let's evaluate {{{f(5)}}}

{{{f(5)=2(5)^2-4(5)-6}}} Plug in {{{n=5}}}. In other words, replace each n with 5.

{{{f(5)=2(25)-4(5)-6}}} Evaluate {{{(5)^2}}} to get 25.

{{{f(5)=+50-4(5)-6}}} Multiply 2 and 25 to get  50

{{{f(5)=+50-20-6}}} Multiply -4 and 5 to get  -20

{{{f(5)=24}}} 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> -5</TD><TD>64</TD></TR>
<TR><TD> -4</TD><TD>42</TD></TR>
<TR><TD> -3</TD><TD>24</TD></TR>
<TR><TD> -2</TD><TD>10</TD></TR>
<TR><TD> -1</TD><TD>0</TD></TR>
<TR><TD> 0</TD><TD>-6</TD></TR>
<TR><TD> 1</TD><TD>-8</TD></TR>
<TR><TD> 2</TD><TD>-6</TD></TR>
<TR><TD> 3</TD><TD>0</TD></TR>
<TR><TD> 4</TD><TD>10</TD></TR>
<TR><TD> 5</TD><TD>24</TD></TR>
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-10,10,-10,10,
grid( 1 ),
circle(-5,64,0.05),
circle(-5,64,0.08),
circle(-4,42,0.05),
circle(-4,42,0.08),
circle(-3,24,0.05),
circle(-3,24,0.08),
circle(-2,10,0.05),
circle(-2,10,0.08),
circle(-1,0,0.05),
circle(-1,0,0.08),
circle(0,-6,0.05),
circle(0,-6,0.08),
circle(1,-8,0.05),
circle(1,-8,0.08),
circle(2,-6,0.05),
circle(2,-6,0.08),
circle(3,0,0.05),
circle(3,0,0.08),
circle(4,10,0.05),
circle(4,10,0.08),
circle(5,24,0.05),
circle(5,24,0.08))}}}

Now connect the points to graph {{{y=2n^2-4n-6}}} (just replace n with x) (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, 2x^2-4x-6),
circle(-5,64,0.05),
circle(-5,64,0.08),
circle(-4,42,0.05),
circle(-4,42,0.08),
circle(-3,24,0.05),
circle(-3,24,0.08),
circle(-2,10,0.05),
circle(-2,10,0.08),
circle(-1,0,0.05),
circle(-1,0,0.08),
circle(0,-6,0.05),
circle(0,-6,0.08),
circle(1,-8,0.05),
circle(1,-8,0.08),
circle(2,-6,0.05),
circle(2,-6,0.08),
circle(3,0,0.05),
circle(3,0,0.08),
circle(4,10,0.05),
circle(4,10,0.08),
circle(5,24,0.05),
circle(5,24,0.08))}}}```