Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).

9514 1404 393

  f, h, g

Step-by-step explanation:

The axis of symmetry for a vertically-opening parabola is the line ...

  x = constant

where the constant is the x-coordinate of the vertex.

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h(x)

The equation of f(x) is given in vertex form ...

  f(x) = a(x -h)² +k . . . . . vertex: (h, k)

where (h, k) = (-4, 1).

The axis of symmetry of f(x) is x = -4.

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g(x)

The equation of g(x) is given in standard form ...

  g(x) = ax² +bx +c

The line of symmetry for this parabola is ...

  x = -b/(2a) = -(-16)/(2(2)) = 16/4 = 4

The axis of symmetry of g(x) is x = 4.

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h(x)

The x-coordinate of the vertex can be read from the graph:

  x = 1

The axis of symmetry of h(x) is x = 1.

__

From smallest to largest, the rank is f(x), h(x), g(x).

$ 1,965,334

Step-by-step explanation:

Annual sales of company in 1999 = $ 1,200,000

Geometric mean growth rate = 10.37 % = 0.1037

In order to forecast we have to use the concept of Geometric sequence. The annual sales of company in 1999 constitute the first term of the sequence, so:

The growth rate is 10.37% more, this means compared to previous year the growth factor will be

r =1 + 0.1037 = 1.1037

We have to forecast the sales in 2004 which will be the 6th term of the sequence with 1999 being the first term. The general formula for n-th term of the sequence is given as:

So, for 6th term or the year 2004, the forecast will be:

Thus, the forecasted sales for 2004 are $ 1,965,334