I wrote the following function to find the longest palindrome in a string. It works fine but it won't work for words like noon or redder. I fiddled around and changed the first line in the for loop from:

var oddPal = centeredPalindrome(i, i);

to

var oddPal = centeredPalindrome(i-1, i);

and now it works, but I'm not clear on why. My intuition is that if you are checking an odd-length palindrome it will have one extra character in the beginning (I whiteboarded it out and that's the conclusion I came to). Am I on the right track with my reasoning?

var longestPalindrome = function(string) {



  var length = string.length;

  var result = ;



  var centeredPalindrome = function(left, right) {

    while (left >= 0 && right < length && string[left] === string[right]) {

      //expand in each direction.

      left--;

      right++;

    }



    return string.slice(left + 1, right);

  }; 



  for (var i = 0; i < length - 1; i++) {

    var oddPal = centeredPalindrome(i, i); 

    var evenPal = centeredPalindrome(i, i);



    if (oddPal.length > result.length)

      result = oddPal;

    if (evenPal.length > result.length)

      result = evenPal;

  }



  return the palindrome is:  + result +  and its length is:  + result.length;

};

UPDATE:
After Paul's awesome answer, I think it makes sense to change both variables for clarity:

var oddPal  = centeredPalindrome(i-1, i + 1);

var evenPal = centeredPalindrome(i, i+1);