Question 130124
Do you want to graph?


In order to graph {{{f(x)=-2x^2-8x+3}}}, 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)=-2x^2-8x+3}}} Start with the given function



{{{f(-5)=-2(-5)^2-8(-5)+3}}} Plug in {{{x=-5}}}



{{{f(-5)=-2*25-8*-5+3}}} Raise -5 to the 2nd power to get 25



{{{f(-5)=-50-8*-5+3}}} Multiply -2 and 25 to get -50



{{{f(-5)=-50--40+3}}} Multiply 8 and -5 to get -40



{{{f(-5)=-10+3}}} Subtract -40 from -50 to get -10



{{{f(-5)=-7}}} Add -10 and 3 to get -7



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



So our 1st point is (-5,-7)



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



{{{f(x)=-2x^2-8x+3}}} Start with the given function



{{{f(-4)=-2(-4)^2-8(-4)+3}}} Plug in {{{x=-4}}}



{{{f(-4)=-2*16-8*-4+3}}} Raise -4 to the 2nd power to get 16



{{{f(-4)=-32-8*-4+3}}} Multiply -2 and 16 to get -32



{{{f(-4)=-32--32+3}}} Multiply 8 and -4 to get -32



{{{f(-4)=0+3}}} Subtract -32 from -32 to get 0



{{{f(-4)=3}}} Add 0 and 3 to get 3



So when {{{x=-4}}}, we have {{{y=3}}}



So our 2nd point is (-4,3)



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



{{{f(x)=-2x^2-8x+3}}} Start with the given function



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



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



{{{f(-3)=-18-8*-3+3}}} Multiply -2 and 9 to get -18



{{{f(-3)=-18--24+3}}} Multiply 8 and -3 to get -24



{{{f(-3)=6+3}}} Subtract -24 from -18 to get 6



{{{f(-3)=9}}} Add 6 and 3 to get 9



So when {{{x=-3}}}, we have {{{y=9}}}



So our 3rd point is (-3,9)



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



{{{f(x)=-2x^2-8x+3}}} Start with the given function



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



{{{f(-2)=-2*4-8*-2+3}}} Raise -2 to the 2nd power to get 4



{{{f(-2)=-8-8*-2+3}}} Multiply -2 and 4 to get -8



{{{f(-2)=-8--16+3}}} Multiply 8 and -2 to get -16



{{{f(-2)=8+3}}} Subtract -16 from -8 to get 8



{{{f(-2)=11}}} Add 8 and 3 to get 11



So when {{{x=-2}}}, we have {{{y=11}}}



So our 4th point is (-2,11)



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



{{{f(x)=-2x^2-8x+3}}} Start with the given function



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



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



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



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



{{{f(-1)=6+3}}} Subtract -8 from -2 to get 6



{{{f(-1)=9}}} Add 6 and 3 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)=-2x^2-8x+3}}} Start with the given function



{{{f(0)=-2(0)^2-8(0)+3}}} Plug in {{{x=0}}}



{{{f(0)=-2*0-8*0+3}}} Raise 0 to the 2nd power to get 0



{{{f(0)=0-8*0+3}}} Multiply -2 and 0 to get 0



{{{f(0)=0-0+3}}} Multiply 8 and 0 to get 0



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



{{{f(0)=3}}} Add 0 and 3 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)=-2x^2-8x+3}}} Start with the given function



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



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



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



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



{{{f(1)=-10+3}}} Subtract 8 from -2 to get -10



{{{f(1)=-7}}} Add -10 and 3 to get -7



So when {{{x=1}}}, we have {{{y=-7}}}



So our 7th point is (1,-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> -5</TD><TD>-7</TD></TR> 
<TR><TD> -4</TD><TD>3</TD></TR> 
<TR><TD> -3</TD><TD>9</TD></TR> 
<TR><TD> -2</TD><TD>11</TD></TR> 
<TR><TD> -1</TD><TD>9</TD></TR> 
<TR><TD> 0</TD><TD>3</TD></TR> 
<TR><TD> 1</TD><TD>-7</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
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),
circle(-4,3,0.05),
circle(-4,3,0.08),
circle(-4,3,0.05),
circle(-4,3,0.1),
circle(-4,3,0.05),
circle(-4,3,0.12),
circle(-3,9,0.05),
circle(-3,9,0.08),
circle(-3,9,0.05),
circle(-3,9,0.1),
circle(-3,9,0.05),
circle(-3,9,0.12),
circle(-2,11,0.05),
circle(-2,11,0.08),
circle(-2,11,0.05),
circle(-2,11,0.1),
circle(-2,11,0.05),
circle(-2,11,0.12),
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(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,-7,0.05),
circle(1,-7,0.08),
circle(1,-7,0.05),
circle(1,-7,0.1),
circle(1,-7,0.05),
circle(1,-7,0.12)
)}}}



Now connect the points to graph {{{y=-2x^2-8x+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, -2x^2-8x+3),
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),
circle(-4,3,0.05),
circle(-4,3,0.08),
circle(-4,3,0.05),
circle(-4,3,0.1),
circle(-4,3,0.05),
circle(-4,3,0.12),
circle(-3,9,0.05),
circle(-3,9,0.08),
circle(-3,9,0.05),
circle(-3,9,0.1),
circle(-3,9,0.05),
circle(-3,9,0.12),
circle(-2,11,0.05),
circle(-2,11,0.08),
circle(-2,11,0.05),
circle(-2,11,0.1),
circle(-2,11,0.05),
circle(-2,11,0.12),
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(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,-7,0.05),
circle(1,-7,0.08),
circle(1,-7,0.05),
circle(1,-7,0.1),
circle(1,-7,0.05),
circle(1,-7,0.12)
)}}}