SOLUTION: I am having trouble finding book help and with my notes to learn/solve this problem. Graph each equation: Y=1/2xsquared Can you help me?

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Question 187667This question is from textbook Mathematical Excursions
: I am having trouble finding book help and with my notes to learn/solve this problem.
Graph each equation:
Y=1/2xsquared
Can you help me? This question is from textbook Mathematical Excursions

Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Graph each equation:
Y=1/2xsquared
-----------------
get the (free) software to make graphs at
http://www.padowan.dk/graph/

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=%281%2F2%29x%5E2, we need to plot a few points


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%28-4%29%5E2 Plug in x=-4.


y=%281%2F2%29%2816%29 Square -4 to get 16.


y=%2816%29%2F2 Multiply.


y=8 Reduce.


So if x=-4, then y=8


This means that we have the point (-4,8)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%28-3%29%5E2 Plug in x=-3.


y=%281%2F2%29%289%29 Square -3 to get 9.


y=%289%29%2F2 Multiply.


y=4.5 Divide.


So if x=-3, then y=4.5


This means that we have the point (-3,4.5)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%28-2%29%5E2 Plug in x=-2.


y=%281%2F2%29%284%29 Square -2 to get 4.


y=%284%29%2F2 Multiply.


y=2 Reduce.


So if x=-2, then y=2


This means that we have the point (-2,2)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%28-1%29%5E2 Plug in x=-1.


y=%281%2F2%29%281%29 Square -1 to get 1.


y=%281%29%2F2 Multiply.


y=0.5 Divide.


So if x=-1, then y=0.5


This means that we have the point (-1,0.5)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%280%29%5E2 Plug in x=0.


y=%281%2F2%29%280%29 Square 0 to get 0.


y=%280%29%2F2 Multiply.


y=0 Reduce.


So if x=0, then y=0


This means that we have the point (0,0)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%281%29%5E2 Plug in x=1.


y=%281%2F2%29%281%29 Square 1 to get 1.


y=%281%29%2F2 Multiply.


y=0.5 Divide.


So if x=1, then y=0.5


This means that we have the point (1,0.5)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%282%29%5E2 Plug in x=2.


y=%281%2F2%29%284%29 Square 2 to get 4.


y=%284%29%2F2 Multiply.


y=2 Reduce.


So if x=2, then y=2


This means that we have the point (2,2)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%283%29%5E2 Plug in x=3.


y=%281%2F2%29%289%29 Square 3 to get 9.


y=%289%29%2F2 Multiply.


y=4.5 Divide.


So if x=3, then y=4.5


This means that we have the point (3,4.5)


---------------------------------------------


y=%281%2F2%29x%5E2 Start with the given equation.


y=%281%2F2%29%284%29%5E2 Plug in x=4.


y=%281%2F2%29%2816%29 Square 4 to get 16.


y=%2816%29%2F2 Multiply.


y=8 Reduce.


So if x=4, then y=8


This means that we have the point (4,8)


---------------------------------------------


Now lets make a table of the values we have calculated:


xy
-48
-34.5
-22
-10.5
00
10.5
22
34.5
48



Now let's plot the points:



---------------------------------------------------------------------


Now draw a curve through all of the points to graph y=%281%2F2%29x%5E2:


Graph of y=%281%2F2%29x%5E2