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 $y = \frac{1}{18} (x -4 )^2 + 3.5$

The  domain is  [1, 7]

Step-by-step 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)

       $4 = b(7-4)^2 + 3.5$

     $4 = 9b + 3.5$

      $b = \frac{1}{18}$

Generally the function that define the given graph is

      $y = \frac{1}{18} (x -4 )^2 + 3.5$

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]