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Describe the function `f(x)= 1/2x^2`

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roshan-rox | Valedictorian

Posted June 10, 2013 at 7:48 AM via web

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Describe the function `f(x)= 1/2x^2`

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted June 10, 2013 at 7:57 AM (Answer #1)

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`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

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