SOLUTION: y=-x^2 y=-4x^2 y=-6x^2

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Question 133355This question is from textbook
: y=-x^2
y=-4x^2
y=-6x^2 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to graph these? I'll do the first two to get you started.

# 1

In order to graph f%28x%29=-1x%5E2, 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%28x%29=-1x%5E2 Start with the given function


f%28-3%29=-1%28-3%29%5E2 Plug in x=-3


f%28-3%29=-1%2A9 Raise -3 to the 2nd power to get 9


f%28-3%29=-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%28x%29=-1x%5E2 Start with the given function


f%28-2%29=-1%28-2%29%5E2 Plug in x=-2


f%28-2%29=-1%2A4 Raise -2 to the 2nd power to get 4


f%28-2%29=-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%28x%29=-1x%5E2 Start with the given function


f%28-1%29=-1%28-1%29%5E2 Plug in x=-1


f%28-1%29=-1%2A1 Raise -1 to the 2nd power to get 1


f%28-1%29=-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%28x%29=-1x%5E2 Start with the given function


f%280%29=-1%280%29%5E2 Plug in x=0


f%280%29=-1%2A0 Raise 0 to the 2nd power to get 0


f%280%29=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%28x%29=-1x%5E2 Start with the given function


f%281%29=-1%281%29%5E2 Plug in x=1


f%281%29=-1%2A1 Raise 1 to the 2nd power to get 1


f%281%29=-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%28x%29=-1x%5E2 Start with the given function


f%282%29=-1%282%29%5E2 Plug in x=2


f%282%29=-1%2A4 Raise 2 to the 2nd power to get 4


f%282%29=-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%28x%29=-1x%5E2 Start with the given function


f%283%29=-1%283%29%5E2 Plug in x=3


f%283%29=-1%2A9 Raise 3 to the 2nd power to get 9


f%283%29=-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 



 xy



 -3-9
 

 -2-4
 

 -1-1
 

 00
 

 1-1
 

 2-4
 

 3-9
Now plot the points



Now connect the points to graph y=-1x%5E2 (note: the more points you plot, the easier it is to draw the graph)






In order to graph f%28x%29=-4x%5E2, 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%28x%29=-4x%5E2 Start with the given function


f%28-1%29=-4%28-1%29%5E2 Plug in x=-1


f%28-1%29=-4%2A1 Raise -1 to the 2nd power to get 1


f%28-1%29=-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%28x%29=-4x%5E2 Start with the given function


f%280%29=-4%280%29%5E2 Plug in x=0


f%280%29=-4%2A0 Raise 0 to the 2nd power to get 0


f%280%29=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%28x%29=-4x%5E2 Start with the given function


f%281%29=-4%281%29%5E2 Plug in x=1


f%281%29=-4%2A1 Raise 1 to the 2nd power to get 1


f%281%29=-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 



 xy



 -1-4
 

 00
 

 1-4
Now plot the points



Now connect the points to graph y=-4x%5E2 (note: the more points you plot, the easier it is to draw the graph)