The function g(n) = n2 − 20n + 95 represents a parabola. part a: rewrite the function in vertex form by completing the square. show your work. (6 points) part b: determine the vertex and indicate whether it is a maximum or a minimum on the graph. how do you know? (2 points) part c: determine the axis of symmetry for g(n). (2 points)

A. The function is now in standard form with a=1, b=-20 and c=95. get to vertex form g(n) = a(x-h)² + k, there is a simple transformation you can remember:

h = -b/2a and k=g(h).

h=10 and k=100 - 200 + 95 = -5, so g(n) = (n-10)²-5

If you don't want to use that formula, just equate a(n-h)² + k to an²+bn+c and you can derive the same thing for yourself.

B. In the vertex form, finding the vertex is trivial. It is at (h,k), ie., (10,-5). It is a minimum because the sign of a (ie the sign at the n² term) is positive.

C. The axis of symmetry is the n value of the vertex, ie., n=10