Higher order polynomial functions, cubic, quartic, quintic, and so on, have curved graphs. The methods for finding the axis crossings for these functions are similar to the methods used above for the quadratic function.
Zeroes
The zeroes of a function are the points at which its graph touches the x-axis. The graph of a polynomial of degree n has at most n zeroes. The zeroes of a function may be found by factoring the polynomial. The zero of each linear factor is a point on the x-axis which the graph touches.
For example, the polynomial function below can be factored:
f(x) = x3 + 2x2 - 5x - 6
= (x + 3)(x + 1)(x - 2)
Then, it has zeroes at:
Now consider the function:x = -3, -1, 2
It can be factored as:f(x) = x3 + 4x2 + 6x + 4
It has two complex roots, so the graph crosses the x-axis only at {0, -2}.f(x) = (x + 2)(x + 1 - i)(x + 1 + i)