Quadratic functions

For each of the following functions, find the vertex, axis, domain, range, intercepts, and sketch the graph.

Mathematical romance

One romantic evening in front of a warm fireplace, your sweetheart turns to you and says: “I will marry you if you can solve my mathematical challenge. Consider a multidigit integer N that is a power of 2. Moreover, each digit of N is also a power of 2. What is N ?”
You think about it, but no solution pop into your head.
Your lover sighs, massages the back of your neck, and finally whispers: “If you do not answer correctly, I will seek a more intelligent mate.”
Can you satisfy your potential spouse ?

The square root symbol

The Austrian mathematician Christoff Rudolff was the first to use the square root in print; it was published in 1525 in DIE COSS