Yes. An iPhone app will open and function on an iPad. The app will simply be scaled up to fill the larger screen or it will appear in the center of the screen with black borders around it, depending on the user’s preference.
If you want your app to take advantage of the extra screen real estate available on an iPad, we may need to do some additional iPad app development to add extra elements or functionality to take advantage of the extra screen real estate.
An app can usually be optimised for iPad for around 50% of the initial iPhone development cost. Same goes for Android and Android tablets.