Out the box Ivory Search allows you to display your search forms in multiple places as listed below.
Display Search Form In Sidebar Or Widget Area
Apart from above listed places, If you want to display search form on any custom location then you can do so by adding below PHP code in your site child theme file or using it in any of your custom plugin.
echo do_shortcode( '[ivory-search id="1707"]' );
Please change the 1707 id in the above code with the search form ID that you want to display.