Hannah jumped from the side of the pool and Dove under the water 4 ft from the pool side. She came out of the water 12 ft away from the poolside. Her path under the water was in the shape of a parabola. If the X intercepts are the points where she entered and exited the water, finally access of the Symmetry by looking at the graph of the x-intercepts. How far from where she entered the water was Hannah when she reached her lowest point in the pool? What is the axis of symmetry? What is the distance?

We are told that she jumped from the side of the pool and the point at which she made contact with the water to dive under was a distance of 4 ft horizontal from the pool side. Secondly, the point at which she came out of the pool was 12 ft from the pool side.

Thus, since the points where she came out and where she dove into the pool are the x-intercepts, then it means that the factors of the parabola formed are; (x - 4) and (x - 12)

Thus, the quadratic equation formed by the parabola is;

y = (x - 4) * (x - 12)

y = x² - 16x + 48

Now, the coordinates for the vertex will be (h, k).

h = -b/2a

h = -(-16)/(2 * 1)

h = 8

k = 8² - 16(8) + 48

k = -16

Thus, the distance from where she entered the water to when she reached her lowest point in the pool is 16 ft

The axis of symmetry is x = 8 ft

Read more about Parabola Vertex at; https://brainly.com/question/1480401

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