SOLUTION: how do you make a table and graph the function f(x)=1/2 of x squared

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Question 485854: how do you make a table and graph the function f(x)=1/2 of x squared
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is y = x^2/2
your graph would look like this:
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2F2%29
you set up a table with values of x and corresponding values of y.
your table would look like this:
x	y = x^2/2
-10	50
-9	40.5
-8	32
-7	24.5
-6	18
-5	12.5
-4	8
-3	4.5
-2	2
-1	0.5
0	0
1	0.5
2	2
3	4.5
4	8
5	12.5
6	18
7	24.5
8	32
9	40.5
10	50

if you knew the shape of the curve, you might have been able to get by with plotting less values of x and then finding the corresponding value of y by using the equation.

example:
equation is y = x^2/2
when x is equal to 5, y is equal to 5^2/2 = 25/2 = 12.5

since y = x^2 is a form of the quadratic equation, then you could have determined the general shape just from that fact alone.

you do need to be familiar with what the graph of a quadratic equation looks like in order to be able to minimize the number of points you need to sketch the graph.

if in doubt, start with x = 0 and work up and down in increments of 1 to see if a shape develops.

sometimes you need more values of x to see if a shape develops.

in this case, x from -5 to + 5 would probably have been enough.

jumping to x = -10 and x = +10 would have been enough to show that it's was following the same trajectory as the values of x got bigger or smaller.

the minimum point is at x = 0.

you could see a change in direction when you plotted values of x = 0, then x = -1, then x = 1.