As stated in the question comments, this is a browser / client side issue. PHP is a server side scripting language.
However, in you code, try this instead:
<?php
function showImage() {
$my_img = imagecreate( 200, 80 );
$background = imagecolorallocate( $my_img, 0, 0, 255 );
$text_colour = imagecolorallocate( $my_img, 255, 255, 0 );
$line_colour = imagecolorallocate( $my_img, 128, 255, 0 );
imagestring( $my_img, 4, 30, 25, "Quote", $text_colour );
imagesetthickness ( $my_img, 5 );
imageline( $my_img, 30, 45, 165, 45, $line_colour );
//header( "Content-type: image/png" );
imagepng( $my_img, "quote.png" );
imagecolordeallocate( $line_color );
imagecolordeallocate( $text_color );
imagecolordeallocate( $background );
// You should call this too.
imagedestroy($my_img);
echo '<a href="quote.png" target="_blank">View the image</a>';
// Or, you could try:
// echo '<html><body><script>window.open('quote.png','_blank')</script></body></html>';
}
?>