How to record values in html form to email adress

Question

I'm making a website and i want to send the values inputed into a contact form directly to my email. I already have a php script for it but it never sends any email any help will be greatly appreciated. the html form:

<form role="form" id="contactForm" class="contact-form" data-toggle="validator" class="shake">
<div class="col-sm-7 slideanim" method="post" action="php-core/mail-core.php">
  <div class="row">
    <div class="col-sm-6 form-group">
        <div class="controls">
            <input class="form-control" id="name" name="name" placeholder="Name" type="text" required required data-error="Please enter your name">
            <div class="help-block with-errors"></div>
        </div>
    </div>
    <div class="col-sm-6 form-group">
        <div class="controls">
            <input class="form-control" id="email" name="email" placeholder="Email" type="email" required required data-error="Please enter your email">
            <div class="help-block with-errors"></div>
        </div>
    </div>
    <div class="col-sm-6 form-group">
        <div class="controls">
            <input type="text" id="msg_subject" class="form-control" placeholder="Subject" required data-error="Please enter your message subject">
            <div class="help-block with-errors"></div>
        </div>
    </div>
    <div class="col-sm-6 form-group">
        <div class="controls">
            <input class="form-control" id="phone" name="phone" placeholder="Phone Number" type="tel" required required data-error="Please enter your Phone Number">
            <div class="help-block with-errors"></div>
        </div>
    </div>
  </div>
    <div class="form-group">
        <div class="controls">
            <textarea class="form-control" id="message" name="message" placeholder="Message" rows="5" required data-error="Write your message"></textarea><br>
            <div class="help-block with-errors"></div>
        </div>
    </div>
    <div class="row">
    <div class="col-sm-12 form-group">
        <button class="btn btn-default pull-right" type="submit" id="submit">Send</button>
        <div id="msgSubmit" class="h3 text-center hidden"></div>
        <div class="clearfix"  style="padding-bottom: 20px;"></div>
    </div>
  </div>
</div>
</form>

the php script:

<?php
if(!isset($_POST['submit']))
{
    //This page should not be accessed directly. Need to submit the form.
    echo "error; you need to submit the form!";
}
$name = $_POST['name'];
$visitor_email = $_POST['email'];
$message = $_POST['message'];

//Validate first
if(empty($name)||empty($visitor_email)) 
{
    echo "Name and email are mandatory!";
    exit;
}

if(IsInjected($visitor_email))
{
    echo "Bad email value!";
    exit;
}

$email_from = $_POST['name'];//<== update the email address
$email_subject = "New Form submission";
$email_body = "You have received a new message from the user:- \n\nName: $name \n".
"Email Address: $visitor_email \n".
    "Message: $message \n";

$to = "Sparkidea1@yahoo.com";//<== update the email address
$from = "Reply-To: $visitor_email";
$headers .= "\r\n Reply-To: $visitor_email \r\n";
//Send the email!
mail($to,$email_subject,$email_body,$from);
//done. redirect to thank-you page.
header('Location: bat/thank-you.html');


// Function to validate against any email injection attempts
function IsInjected($str)
{
  $injections = array('(\n+)',
              '(\r+)',
              '(\t+)',
              '(%0A+)',
              '(%0D+)',
              '(%08+)',
              '(%09+)'
              );
  $inject = join('|', $injections);
  $inject = "/$inject/i";
  if(preg_match($inject,$str))
    {
    return true;
  }
  else
    {
    return false;
  }
}

?> 

it doesn't give errors but it does not send mails help please...thanks!