Question

The function g(n) = n2 − 16n + 69 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)

Answer 1

A) n^2 -16n+69 = (n-8)^2 - 64 + 69 = (n-8)^2+5
B) vertex (n,g(n)) = (8, 5). It's a minimum because for any other value of n, (n-8)^2 is positive and it adds (positive sign before the ()^2)
C) n=8 is the axis of symmetry (it is the horizontal value of the vertex)

Answer 2

Answer:

function in vertex form is: $g(n)=(n-8)^2+5$

vertex is: (8,5) and is a minimum on the graph.

axis of symmetry is x=8.

Step-by-step explanation:

A:

$g(n)=n^2-16n+69\\g(n)=(n-8)^2+5$

Hence $g(n)=(n-8)^2+5$ is the vertex form of the given function g(n).

B:  Hence the vertex of any equation of the type $y=a(x-h)^2+k$ is given by (h,k)

so, the vertex here is :(8,5)

this is a upward open parabola so the vertex has a minimum hence (8,5) are the minimum point of the graph.

C: The axis of symmetry of a parabola is a straight line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.

here the axis of symmetry is a vertical line that passes through the vertex.hence the value of x is fixed.

so equation of axis of symmetry is: $x=8$