Don't know much about blade but a checkbox is a one or zero so I
<tr>
<td>Adopted:</td>
<?php
if ($data['row'][0]->adopted == 1) {
echo "<td>";
echo "<input type=\"checkbox\" name=\"adopted\" id=\"adopted\" value=\"1\" checked />";
echo "</td>";
} else {
echo "<td>";
echo "<input type=\"checkbox\" name=\"adopted\" id=\"adopted\" />";
echo "</td>";
}
?>
</tr>
and test for a check
$adopted = (isset($_POST['adopted']) == '1' ? '1' : '0');
If not checked, nothing passes in php, so that will be a nothing value.