trigger QuoteSentTrigger on Task (after insert) {
 Map<ID,Datetime> QuoteSentMap = new Map<ID,Datetime>(); //this will map all affected Accounts by add and task createdby date
 
 //loop through all tasks in this transaction to support bulk load
 for(Task newTask:Trigger.new){
                //assumes the subject line you are looking for is 'Quote Sent' 
  if(newTask.Subject.equals('Quote Sent')){
                        //checks to make sure the task is somehow related to an account
   if(!(newTask.Accountid==null)){
    QuoteSentMap.put(newTask.Accountid,newTask.CreatedDate);
   }
  }
 }
 //this will retrieve all Accounts that need to be updated, and assumes quotedate field on Account record has that api name and is a datetime type
 List<Account> updAccts = [select id,last_quote_sent__c from Account where id in :QuoteSentMap.keyset()];
 if(UpdAccts.size()>0){
  for(Account a:updAccts){
   a.last_quote_sent__c=QuoteSentMap.get(a.id);  //set the field to the new value
  }
  try{
   update updAccts;  //update all account records with one DML statement
  }catch(DMLException e){
   system.debug('\n\nERROR Updating Accounts:'+e.getDMLMessage(0));//catch any errors that might occur
  }
 } 
}

/**
 * This class contains unit tests for validating the behavior of Apex classes
 * and triggers.
 *
 * Unit tests are class methods that verify whether a particular piece
 * of code is working properly. Unit test methods take no arguments,
 * commit no data to the database, and are flagged with the testMethod
 * keyword in the method definition.
 *
 * All test methods in an organization are executed whenever Apex code is deployed
 * to a production organization to confirm correctness, ensure code
 * coverage, and prevent regressions. All Apex classes are
 * required to have at least 75% code coverage in order to be deployed
 * to a production organization. In addition, all triggers must have some code coverage.
 * 
 * The @isTest class annotation indicates this class only contains test
 * methods. Classes defined with the @isTest annotation do not count against
 * the organization size limit for all Apex scripts.
 *
 * See the Apex Language Reference for more information about Testing and Code Coverage.
 */
@isTest
private class TestQuoteSentTrigger {

    static testMethod void myUnitTest() {
        String TestAcctID='';
        String TestTaskID='';
        Account testAcct = new Account(name='Test Account');//create a test account for portability
        try{
         insert testAcct;
         TestAcctID=testAcct.ID;
        }catch(DMLException e){
         system.debug('\n\nError occurred inserting test account:'+e.getDMLMessage(0));
        }
        Task testTask = new Task(subject='Quote Sent',whatid=TestAcctID);//create new task for testing, related to test account
        try{
         insert testTask;
         TestTaskID=testTask.id;
        }catch(DMLException e){
         system.debug('\n\nError occurred inserting test task:'+e.getDMLMessage(0));
        }
        //Validate that our trigger worked
        Account checkAcct= [select id,last_quote_sent__c from Account where id =:TestAcctID];
        system.debug('\n\nTest Account: '+checkAcct);
        Task checkTask=[select id,createddate from Task where id=:TestTaskID];
        system.debug('\n\nTest Task'+checkTask);
        system.assertequals(checkAcct.last_quote_sent__c,checkTask.createddate);
    }
}