How does the rate of cooling in a magma influence the crystallization of minerals in an igneous rock? give examples of each texture and how they might form?

The crystallization process depends from the cooling off of the magma.

When the cooling off is on the surface, then it's quick, the crystals that are forming are very small. These rocks are extrusive rocks. Some of the most recognizable extrusive rocks are basalt, andesite, obsidian ...

When the cooling of is deep bellow the surface, then it's slow, the rocks are under bigger temperature and pressure, and the crystals will be big. These rocks are intrusive rocks. Some of the most recognizable are granite, diorite, gabbro ...