Find K biggest numbers in the array
Store the first k elements in a temporary array temp[0..k-1]  


You are not doing that  


  Find the smallest element in temp[], let the smallest element be min


You are not doing that  


  For each element x in arr[k] to arr[n-1]...


You are starting on 0 because you skipped step 1

Nothing in there about a binary search
Not less operations the with the shifts

This 

if (testArray[i] &lt;= result[0])
{
    continue;
}
else
{


Can be  

if (testArray[i] &gt; result[0])
{


Other than that looks good

Just following what I think are the instructions
It is \$\mathcal{O}(n \times k)\$ as the first k elements are not free 

private int[] FindKBiggestNumbersM(int[] testArray, int k)
{
    int[] result = new int[k];
    int indexMin = 0;
    result[indexMin] = testArray[0];
    int min = result[indexMin];

    for (int i = 1; i &lt; testArray.Length; i++)
    {
        if(i &lt; k)
        {
            result[i] = testArray[i];
            if (result[i] &lt; min)
            {
                min = result[i];
                indexMin = i;
            }
        }
        else if (testArray[i] &gt; min)
        {
            min = testArray[i];
            result[indexMin] = min;
            for (int r = 0; r &lt; k; r++)
            {
                if (result[r] &lt; min)
                {
                    min = result[r];
                    indexMin = r;
                }
            }
        }
    }
    return result;
}