Students noticed that the path of water from a water fountain seemed to form a parabolic arc. They set a flat surface at the level of the water spout and measured the maximum height of the water from the flat surface as 6 inches and the distance from the spout to where the water hit the flat surface as 8 inches. Construct a function model for the stream of water, where h(x) is the water height x inches from the fountain spout.

Question

Students noticed that the path of water from a water fountain seemed to form a parabolic arc. They set a flat surface at the level of the water spout and measured the maximum height of the water from the flat surface as 6 inches and the distance from the spout to where the water hit the flat surface as 8 inches. Construct a function model for the stream of water, where h(x) is the water height x inches from the fountain spout.

Enter the exact answer.
What I did was make 6 the h and 8 the k and I divided 8 by half to get k=4 since its the distance. I then plugged it in the vertex form a(x-6)^2+4. But I got it wrong so I'm confused. Please Help.

Answer 1

I think it's asking for the function form

Answer 2

what is the function for vertex form?

Answer 3

depends where you want the water spout to be.

It would make sense to have the spout at the origin.
Then the zeros of the function would be (0,0) and (8,0) and the vertex would be at (4,6)

height = a(x - 4)^2 + 6
but (0,0) lies on it, thus:
0 = a(0-4)^2 + 6
16a = -6
a = -3/8

height = (-3/8)(x - 4)^2 + 6

Answer 4

To construct a function model for the stream of water, we can use the equation of a parabola in vertex form: h(x) = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola and "a" determines the shape of the parabola.

In this case, the vertex of the parabola represents the maximum height of the water (6 inches) and the distance from the spout to where the water hits the flat surface (8 inches).

To find the values of "h" and "k," we can use the given information:
- The maximum height (k) is 6 inches.
- The distance from the spout to where the water hits the flat surface (h) is 8 inches.

Therefore, the vertex of the parabola is (8, 6).

Now, let's substitute the vertex coordinates into the equation:
h(x) = a(x - 8)^2 + 6.

To determine the value of "a" and complete the function model, we need additional information.

Please provide any other given details or measurements related to the water fountain, such as the height and distance at other points, or any other equations or conditions mentioned in the problem.