Question 485854
your equation is y = x^2/2
your graph would look like this:
{{{graph(400,400,-10,10,-10,10,x^2/2)}}}
you set up a table with values of x and corresponding values of y.
your table would look like this:
<pre>
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
</pre>
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.