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)

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

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.

Idrk but i think u should figure out the n dia n then the units it will make it way more easier