The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).
If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:
a · 0² + b · 0 + c = 0 (1)
a · 1² + b · 1 + c = 16 (2)
a · 3² + b · 3 + c = 0 (3)
The solution to this system is a = - 8, b = 24, c = 0.
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
To learn more on quadratic functions: https://brainly.com/question/17177510
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