The function g(n) = n^2 − 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)

well, lemme post a quick on how a perfect square trinomial works

as you should already know, now let's look at this equation, and let's start by grouping the variables,

g(n) = n² - 6n + 16

g(n) = (n² - 6n) + 16

g(n) = (n² - 6n + [?]²) + 16

so, we have a missing fellow there, in order to get a perfect square trinomial, well, the tell-tale guy is the middle term, the middle term is the product of 2 and the other two guys without the ², and we know in this case is 6n.

aha!!, there's our missing fellow, is 3.

well, let's keep in mind that all we're doing is borrowing from our very good friend Mr. Zero, 0, so if we add 3², we also have to subtract 3².

is it a maximum of a minimum? well, all we have to do is look at the leading term's sign, n² has a positive coefficient, that means the parabola is opening upwards, assuming "n" is drawn on the x-axis, and since it's opening upwards like a cup, it comes down down down, reaches a minimum and goes back up up up.

well, the axis of symmetry will just be the x-coordinate of the vertex, that is the line that will cut the parabola in two twin halves, namely x = 3.

60 for the first and 130 for the second

step-by-step explanation: