Question 133355
Do you want to graph these? I'll do the first two to get you started.


# 1


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



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



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



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



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



So our 1st point is (-3,-9)



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



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



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



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



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



So when {{{x=-2}}}, we have {{{y=-4}}}



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



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



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



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



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



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



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



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



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



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



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



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



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



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



So our 4th point is (0,0)



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



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



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



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



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



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



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



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



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



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



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



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



So when {{{x=2}}}, we have {{{y=-4}}}



So our 6th point is (2,-4)



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



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



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



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



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



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



So our 7th point is (3,-9)



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

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
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,-4,0.05),
circle(-2,-4,0.08),
circle(-2,-4,0.05),
circle(-2,-4,0.1),
circle(-2,-4,0.05),
circle(-2,-4,0.12),
circle(-1,-1,0.05),
circle(-1,-1,0.08),
circle(-1,-1,0.05),
circle(-1,-1,0.1),
circle(-1,-1,0.05),
circle(-1,-1,0.12),
circle(0,0,0.05),
circle(0,0,0.08),
circle(0,0,0.05),
circle(0,0,0.1),
circle(0,0,0.05),
circle(0,0,0.12),
circle(1,-1,0.05),
circle(1,-1,0.08),
circle(1,-1,0.05),
circle(1,-1,0.1),
circle(1,-1,0.05),
circle(1,-1,0.12),
circle(2,-4,0.05),
circle(2,-4,0.08),
circle(2,-4,0.05),
circle(2,-4,0.1),
circle(2,-4,0.05),
circle(2,-4,0.12),
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)
)}}}



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




<hr>


In order to graph {{{f(x)=-4x^2}}}, 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)=-4x^2}}} Start with the given function



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



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



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



So when {{{x=-1}}}, we have {{{y=-4}}}



So our 1st point is (-1,-4)



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



{{{f(x)=-4x^2}}} Start with the given function



{{{f(0)=-4(0)^2}}} Plug in {{{x=0}}}



{{{f(0)=-4*0}}} Raise 0 to the 2nd power to get 0



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



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



So our 2nd point is (0,0)



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



{{{f(x)=-4x^2}}} Start with the given function



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



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



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



So when {{{x=1}}}, we have {{{y=-4}}}



So our 3rd point is (1,-4)



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

{{{drawing(900,900,-15,15,-15,15,
  grid( 1 ),
circle(-1,-4,0.05),
circle(-1,-4,0.08),
circle(-1,-4,0.05),
circle(-1,-4,0.1),
circle(-1,-4,0.05),
circle(-1,-4,0.12),
circle(0,0,0.05),
circle(0,0,0.08),
circle(0,0,0.05),
circle(0,0,0.1),
circle(0,0,0.05),
circle(0,0,0.12),
circle(1,-4,0.05),
circle(1,-4,0.08),
circle(1,-4,0.05),
circle(1,-4,0.1),
circle(1,-4,0.05),
circle(1,-4,0.12)
)}}}



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