Using Ajax to submit a form, and run a SQL Select query based on user input from the form

I'm creating a web form on my WordPress powered website. The form is intended to allow the user to enter a ZIP Code (aka postal code). When the user submits the form, the page should query a MySQL table, SELECT the rows which match the search criteria and dispense those values into a table on the same page.

Unfortunately, I have been unsuccessful thus far.

Per the example I followed, three components are necessary to query a SQL table from within a WordPress site:

1. A form, written in PHP, which resides in the .php file for your page template
2. A function which actually executes the SQL query, added to your theme's functions.php file
3. A segment of Javascript code to tie the above two things together

Here is what I have so far.

First, the form code:

form type=post action= role=form id=DirectorySearchForm class=DirectorySerch
    p style=font-size: 16pt;Zip Code: input style=font-size: 16pt; type=text name=inZip width=200 height=32/p
    input type=hidden name=action value=DirectorySearch
    input type=submit name=submit value=Search style=font-size: 18pt;
/form
div id=search_results/div

Second, the function in functions.php:

function DirectorySearch() {
    global $wpdb;
    echo 33333;   

    $inZip = $_POST['inZip'];

    $query = 'SELECT OrgName, Phone FROM directory_organizations WHERE Zip_Codes LIKE %s%';

    $results = $wpdb-get_results( $wpdb-prepare($query, $inZip) );
    echo $results;
    die();
}
add_action( 'wp_ajax_DirectorySearch', 'DirectorySearch' );    //If called from admin panel
add_action( 'wp_ajax_nopriv_DirectorySearch', 'DirectorySearch' );    //If called by non-user

Third, the javascript sequence to tie the above two together.

script type=text/javascript
(function($){               
  // get our references
  var $form = $('form.DirectorySerch'),
      $inZip = $('#inZip'),
      $results = $('#search_results');

// on submit, do the search 
  $form.submit(function(e) {
    e.preventDefault();
    do_search();
  });

  // AJAX search call
  function do_search() {

    // grab the query value from the search field
    var search_text = $search_field.val();

    // do a POST ajax call
    $.ajax({
      type: POST,
      url: ?php echo admin_url('admin-ajax.php'); ?,
      data: ({
        action: DirectorySearch,
        search_text: search_text
      }),
      success: function (response){
        console.log(response);
        $results.html(response);
      }     
    });
  }

})(jQuery);
/script

I'm a beginner, so I borrowed heavily from examples of others trying to accomplish the same thing. However, my web form does not generate a query result.

Can anyone see what I might be doing wrong, or, alternatively, advise me on how to troubleshoot?