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olya-2409 [2.1K]
3 years ago
12

The function g(n) = n2 − 16n + 69 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. S

how 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)
Mathematics
2 answers:
EleoNora [17]3 years ago
8 0
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)
kumpel [21]3 years ago
3 0

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


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a) 21-2.58\frac{52}{\sqrt{350}}=13.83  

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So on this case the 99% confidence interval would be given by (13.83;28.17)  

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

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Now we have everything in order to replace into formula (1):  

21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

Part b

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{350}}=7.17

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The margin of error is given by:

ME=2.58\frac{52}{\sqrt{100}}=13.42

Part d

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