Question

You are jumping off the 12-foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water. Your height (h) in feet above the water in terms of (t) seconds is given by h = -16t^2 + 6t + 12. What is the first step in determining the maximum height that you reach during your dive? Question 3 can help you answer this question.

Answer 1

The first step is findind the vertix of the quadratic equation that defines the movement. In the vertix we will have the maximum height.

Vertix: (0.1875, 12.5625)

Maximum height: 12.5625 feet

Explanation:

The first step is findind the vertix of the quadratic equation that defines the movement. In the vertix we will have the maximum height.

To find the vertix, we can use the formula:

x_v = -b/2a

Where 'a' and 'b' are coefficients of the quadratic equation (in this case, a = -16 and b = 6)

So we have that:

x_v = -6 / (-32) = 0.1875

Now, to find the maximum height, we just use this value of x_v for the time t:

h = -16 * (0.1875)^2 + 6*0.1875 + 12 = 12.5625 feet