Polynomial time complexity is the running time complexity of algorithms, which runs to the order of n^k. Quadratic time algorithms are certain types of polynomial time algorithms where k = 2. A very simple example of such an algorithm would be as follows:

for (int i = 0; i <n; i += c) {
    for (int j = 0; j < n; j += c) {
        for (int k = 0; k < n; k += c) {
            // some O(1) expressions
        }
    }
}

As you can see, this example is just an extension of the example in the quadratic time section. The worst case complexity of this case is O(n³).