# When graphing an equation, are all equations to the nth power that are even parabola's?

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So, would #f(x)=4-x^4# be a parabola?

So, would

##### 1 Answer

No

#### Explanation:

No. A parabola is a special kind of graph with the property that for some line (the directrix) and a point not on that line (the focus), every point on the graph is equidistant from the directrix and the focus.

*Any* parabola can be written in the form

where

Notice that this means any polynomial function with degree

The blue graph is the parabola

The red graph is

The green graph is