Tom is jumping off the diving board at the city pool. His height is modeled by the quadratic function h(t) = -16t2 + 16t + 20, where ℎ(t) represents height above water (in feet), and t represents time after jumping (in seconds).

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2022-01-12T12:45:47+01:00

The maximum height attained is 24 feet, and the time to reach this height is 0.5 seconds

A quadratic function is a function that takes any of the following form

[tex]y=ax^2 + bx + c[/tex]

Where:

[tex]a \ne 0[/tex]

The quadratic function is given as:

[tex]h(t) = -16t^2 + 16t + 20[/tex]

To calculate the maximum height, we start by calculating the time to reach the maximum height using:

[tex]t = -\frac {b}{2a}[/tex]

So, we have:

[tex]t = -\frac {16}{2 \times -16}[/tex]

[tex]t = 0.5[/tex]

Substitute 0.5 for t in h(t)

[tex]h(t) = -16t^2 + 16t + 20[/tex]

[tex]h(0.5) = -16(0.5)^2 + 16(0.5) + 20[/tex]

[tex]h(0.5) = 24[/tex]

Hence, the maximum height attained is 24 feet, and the time to reach this height is 0.5 seconds

Read more about quadratic functions at:

https://brainly.com/question/11631534