Question 131611
In order to graph {{{f(x)=1x^2-2x-8}}}, 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^2-2x-8}}} Start with the given function



{{{f(-3)=1(-3)^2-2(-3)-8}}} Plug in {{{x=-3}}}



{{{f(-3)=1*9-2*-3-8}}} Raise -3 to the 2nd power to get 9



{{{f(-3)=9-2*-3-8}}} Multiply 1 and 9 to get 9



{{{f(-3)=9--6-8}}} Multiply 2 and -3 to get -6



{{{f(-3)=15-8}}} Subtract -6 from 9 to get 15



{{{f(-3)=7}}} Subtract 8 from 15 to get 7



So when {{{x=-3}}}, we have {{{y=7}}}



So our 1st point is (-3,7)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(-2)=1(-2)^2-2(-2)-8}}} Plug in {{{x=-2}}}



{{{f(-2)=1*4-2*-2-8}}} Raise -2 to the 2nd power to get 4



{{{f(-2)=4-2*-2-8}}} Multiply 1 and 4 to get 4



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



{{{f(-2)=8-8}}} Subtract -4 from 4 to get 8



{{{f(-2)=0}}} Subtract 8 from 8 to get 0



So when {{{x=-2}}}, we have {{{y=0}}}



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



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(-1)=1(-1)^2-2(-1)-8}}} Plug in {{{x=-1}}}



{{{f(-1)=1*1-2*-1-8}}} Raise -1 to the 2nd power to get 1



{{{f(-1)=1-2*-1-8}}} Multiply 1 and 1 to get 1



{{{f(-1)=1--2-8}}} Multiply 2 and -1 to get -2



{{{f(-1)=3-8}}} Subtract -2 from 1 to get 3



{{{f(-1)=-5}}} Subtract 8 from 3 to get -5



So when {{{x=-1}}}, we have {{{y=-5}}}



So our 3rd point is (-1,-5)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(0)=1(0)^2-2(0)-8}}} Plug in {{{x=0}}}



{{{f(0)=1*0-2*0-8}}} Raise 0 to the 2nd power to get 0



{{{f(0)=0-2*0-8}}} Multiply 1 and 0 to get 0



{{{f(0)=0-0-8}}} Multiply 2 and 0 to get 0



{{{f(0)=0-8}}} Subtract 0 from 0 to get 0



{{{f(0)=-8}}} Subtract 8 from 0 to get -8



So when {{{x=0}}}, we have {{{y=-8}}}



So our 4th point is (0,-8)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(1)=1(1)^2-2(1)-8}}} Plug in {{{x=1}}}



{{{f(1)=1*1-2*1-8}}} Raise 1 to the 2nd power to get 1



{{{f(1)=1-2*1-8}}} Multiply 1 and 1 to get 1



{{{f(1)=1-2-8}}} Multiply 2 and 1 to get 2



{{{f(1)=-1-8}}} Subtract 2 from 1 to get -1



{{{f(1)=-9}}} Subtract 8 from -1 to get -9



So when {{{x=1}}}, we have {{{y=-9}}}



So our 5th point is (1,-9)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(2)=1(2)^2-2(2)-8}}} Plug in {{{x=2}}}



{{{f(2)=1*4-2*2-8}}} Raise 2 to the 2nd power to get 4



{{{f(2)=4-2*2-8}}} Multiply 1 and 4 to get 4



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



{{{f(2)=0-8}}} Subtract 4 from 4 to get 0



{{{f(2)=-8}}} Subtract 8 from 0 to get -8



So when {{{x=2}}}, we have {{{y=-8}}}



So our 6th point is (2,-8)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(3)=1(3)^2-2(3)-8}}} Plug in {{{x=3}}}



{{{f(3)=1*9-2*3-8}}} Raise 3 to the 2nd power to get 9



{{{f(3)=9-2*3-8}}} Multiply 1 and 9 to get 9



{{{f(3)=9-6-8}}} Multiply 2 and 3 to get 6



{{{f(3)=3-8}}} Subtract 6 from 9 to get 3



{{{f(3)=-5}}} Subtract 8 from 3 to get -5



So when {{{x=3}}}, we have {{{y=-5}}}



So our 7th point is (3,-5)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(4)=1(4)^2-2(4)-8}}} Plug in {{{x=4}}}



{{{f(4)=1*16-2*4-8}}} Raise 4 to the 2nd power to get 16



{{{f(4)=16-2*4-8}}} Multiply 1 and 16 to get 16



{{{f(4)=16-8-8}}} Multiply 2 and 4 to get 8



{{{f(4)=8-8}}} Subtract 8 from 16 to get 8



{{{f(4)=0}}} Subtract 8 from 8 to get 0



So when {{{x=4}}}, we have {{{y=0}}}



So our 8th point is (4,0)



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



{{{f(x)=1x^2-2x-8}}} Start with the given function



{{{f(5)=1(5)^2-2(5)-8}}} Plug in {{{x=5}}}



{{{f(5)=1*25-2*5-8}}} Raise 5 to the 2nd power to get 25



{{{f(5)=25-2*5-8}}} Multiply 1 and 25 to get 25



{{{f(5)=25-10-8}}} Multiply 2 and 5 to get 10



{{{f(5)=15-8}}} Subtract 10 from 25 to get 15



{{{f(5)=7}}} Subtract 8 from 15 to get 7



So when {{{x=5}}}, we have {{{y=7}}}



So our 9th point is (5,7)



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>7</TD></TR> 
<TR><TD> -2</TD><TD>0</TD></TR> 
<TR><TD> -1</TD><TD>-5</TD></TR> 
<TR><TD> 0</TD><TD>-8</TD></TR> 
<TR><TD> 1</TD><TD>-9</TD></TR> 
<TR><TD> 2</TD><TD>-8</TD></TR> 
<TR><TD> 3</TD><TD>-5</TD></TR> 
<TR><TD> 4</TD><TD>0</TD></TR> 
<TR><TD> 5</TD><TD>7</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
circle(-3,7,0.05),
circle(-3,7,0.08),
circle(-3,7,0.05),
circle(-3,7,0.1),
circle(-3,7,0.05),
circle(-3,7,0.12),
circle(-2,0,0.05),
circle(-2,0,0.08),
circle(-2,0,0.05),
circle(-2,0,0.1),
circle(-2,0,0.05),
circle(-2,0,0.12),
circle(-1,-5,0.05),
circle(-1,-5,0.08),
circle(-1,-5,0.05),
circle(-1,-5,0.1),
circle(-1,-5,0.05),
circle(-1,-5,0.12),
circle(0,-8,0.05),
circle(0,-8,0.08),
circle(0,-8,0.05),
circle(0,-8,0.1),
circle(0,-8,0.05),
circle(0,-8,0.12),
circle(1,-9,0.05),
circle(1,-9,0.08),
circle(1,-9,0.05),
circle(1,-9,0.1),
circle(1,-9,0.05),
circle(1,-9,0.12),
circle(2,-8,0.05),
circle(2,-8,0.08),
circle(2,-8,0.05),
circle(2,-8,0.1),
circle(2,-8,0.05),
circle(2,-8,0.12),
circle(3,-5,0.05),
circle(3,-5,0.08),
circle(3,-5,0.05),
circle(3,-5,0.1),
circle(3,-5,0.05),
circle(3,-5,0.12),
circle(4,0,0.05),
circle(4,0,0.08),
circle(4,0,0.05),
circle(4,0,0.1),
circle(4,0,0.05),
circle(4,0,0.12),
circle(5,7,0.05),
circle(5,7,0.08),
circle(5,7,0.05),
circle(5,7,0.1),
circle(5,7,0.05),
circle(5,7,0.12)
)}}}



Now connect the points to graph {{{y=1x^2-2x-8}}}  (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^2-2x-8),
circle(-3,7,0.05),
circle(-3,7,0.08),
circle(-3,7,0.05),
circle(-3,7,0.1),
circle(-3,7,0.05),
circle(-3,7,0.12),
circle(-2,0,0.05),
circle(-2,0,0.08),
circle(-2,0,0.05),
circle(-2,0,0.1),
circle(-2,0,0.05),
circle(-2,0,0.12),
circle(-1,-5,0.05),
circle(-1,-5,0.08),
circle(-1,-5,0.05),
circle(-1,-5,0.1),
circle(-1,-5,0.05),
circle(-1,-5,0.12),
circle(0,-8,0.05),
circle(0,-8,0.08),
circle(0,-8,0.05),
circle(0,-8,0.1),
circle(0,-8,0.05),
circle(0,-8,0.12),
circle(1,-9,0.05),
circle(1,-9,0.08),
circle(1,-9,0.05),
circle(1,-9,0.1),
circle(1,-9,0.05),
circle(1,-9,0.12),
circle(2,-8,0.05),
circle(2,-8,0.08),
circle(2,-8,0.05),
circle(2,-8,0.1),
circle(2,-8,0.05),
circle(2,-8,0.12),
circle(3,-5,0.05),
circle(3,-5,0.08),
circle(3,-5,0.05),
circle(3,-5,0.1),
circle(3,-5,0.05),
circle(3,-5,0.12),
circle(4,0,0.05),
circle(4,0,0.08),
circle(4,0,0.05),
circle(4,0,0.1),
circle(4,0,0.05),
circle(4,0,0.12),
circle(5,7,0.05),
circle(5,7,0.08),
circle(5,7,0.05),
circle(5,7,0.1),
circle(5,7,0.05),
circle(5,7,0.12)
)}}}