Question

A red velvet rope hangs between two stanchions and forms a curve that can be modeled by a parabola. In the illustration shown, the unit of measurement for both axes is feet, and the vertex of the curve is point C. Find a quadratic function that models the rope, and state the function's domain.

Answer 1

Complete question

The complete question is shown on the first uploaded image

Answer:

The function is
`y = (1)/(18) (x -4 )^2 + 3.5`

The domain is [1, 7]

Explanation:

Generally from the Graph we can see that

For the y-coordinate the point of symmetry is
`y = g = 4`

For the x-coordinate the point of symmetry is x = 4

The general form of quadratic equation representing this type of curve is

`y = b(x-g)^2 + u`

Now considering the coordinate (4, 3.5) along the axis of symmetry we have that

`3.5 = b(4-4)^2 + u`

=>
`u = 3.5`

Now considering point B having the coordinates (7,4)

`4 = b(7-4)^2 + 3.5`

`4 = 9b + 3.5`

`b = (1)/(18)`

Generally the function that define the given graph is

`y = (1)/(18) (x -4 )^2 + 3.5`

From the graph the first element for x is 1 (i.e [1 . 4] )and the last element for x is 7 (i.e [7,4])

So the domain of the function is [1, 7]