Question 129983
I'm assuming you want to graph {{{f(x)=-3x^2+x-5}}} right?




In order to graph {{{f(x)=-3x^2+x-5}}}, 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)=-3x^2+1x-5}}} Start with the given function



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



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



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



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



{{{f(-1)=-4-5}}} Add -3 and -1 to get -4



{{{f(-1)=-9}}} Subtract 5 from -4 to get -9



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



So our 1st point is (-1,-9)



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



{{{f(x)=-3x^2+1x-5}}} Start with the given function



{{{f(0)=-3(0)^2+1(0)-5}}} Plug in {{{x=0}}}



{{{f(0)=-3*0+1*0-5}}} Raise 0 to the 2nd power to get 0



{{{f(0)=0+1*0-5}}} Multiply -3 and 0 to get 0



{{{f(0)=0+0-5}}} Multiply 1 and 0 to get 0



{{{f(0)=0-5}}} Add 0 and 0 to get 0



{{{f(0)=-5}}} Subtract 5 from 0 to get -5



So when {{{x=0}}}, we have {{{y=-5}}}



So our 2nd point is (0,-5)



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



{{{f(x)=-3x^2+1x-5}}} Start with the given function



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



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



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



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



{{{f(1)=-2-5}}} Add -3 and 1 to get -2



{{{f(1)=-7}}} Subtract 5 from -2 to get -7



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



So our 3rd 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> -1</TD><TD>-9</TD></TR> 
<TR><TD> 0</TD><TD>-5</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(-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,-5,0.05),
circle(0,-5,0.08),
circle(0,-5,0.05),
circle(0,-5,0.1),
circle(0,-5,0.05),
circle(0,-5,0.12),
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=-3x^2+1x-5}}}  (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, -3x^2+1x-5),
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,-5,0.05),
circle(0,-5,0.08),
circle(0,-5,0.05),
circle(0,-5,0.1),
circle(0,-5,0.05),
circle(0,-5,0.12),
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)
)}}}