The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 4 feet, represented by a vertex of (6,4), and lands 12 feet from the water jet, represented by (12,0). Write a function in vertex form that models the path of the stream.

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calculista calculista · Answer 1 · 2019-03-31T23:38:38+02:00

Answer:

y = -4/36 * (x-6)^2 + 4

Step-by-step explanation:

The quadratic equation expressed in vertex from is

y = a(x-h)^2 + k

The vertex is

Vertex = (h,k) = (6,4)

This means

y = a(x-6)^2 + 4

To find a, we know that at 12 feet from the water jet, the height is equal to zero.

0 = a(12-6)^2 + 4

a = -4/36

Therefore, the equation is

y = -4/36 * (x-6)^2 + 4

Please see attached graph for reference.

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raphealnwobi raphealnwobi · Answer 2 · 2022-04-12T10:58:29+02:00

The vertex form that models the path of the stream is y = (-1/9)(x - 6)² + 4

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

Where (h, k) is the vertex

Given the parabola has vertex of (6,4), hence:

y = a(x - 6)² + 4

At point (12, 0):

0 = a(12 - 6)² + 4

a = -1/9.

y = (-1/9)(x - 6)² + 4

The vertex form that models the path of the stream is y = (-1/9)(x - 6)² + 4

Find out more on parabola at: https://brainly.com/question/4148030