Describe the function `f(x)= 1/2x^2`
f(x) will be higher when x increases. But since `x^2 >= 0` the smallest value that `x^2` can get is 0.
So f(x) will be lowest at x = 0.
When x increases f(x) will increase and when x decreases f(x) will increase. When x tends to `+-oo` , f(x) will also go to `+oo` since we have a `x^2` term.
This is shown below graph.
The vertex of the graph is (0,0) and it is a minimum.
As you can see in the graph around x = 0 the graph is symmetrical. So the axis of symmetry is x = 0.
Since the graph intercept x and y axis at origin;
x intercept is x = 0
y intercept is y = 0