The function g(n)=n²-6n+16 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)
(10 points)

Part A

After dividing the first two terms by the coefficient of n², the coefficient of the linear term is -6, so we can complete the square by adding (and subtracting) the square of half that: (-6/2)² = 9.

... g(n) = n² -6n + 9 + 16 - 9

... g(n) = (n -3)² +7 . . . . . . . rewrite to vertex form

Part B

The generic vertex form is

... y = a(x -h)² +k . . . . . . for vertex (h, k) and vertical expansion factor "a"

Comparing this to g(n), we see a=1, h=3, k=7. When a > 0, the parabola opens upward, and the vertex is a minimum. Here, we have a > 0, so we can conclude ...

... the vertex (3, 7) is a minimum

Part C

The axis of symmetry is the vertical line through the vertex.

... x = 3

c.35

step-by-step explanation:

8+13=21

21+8=29

29+6=35