Question

A ball is thrown upward from a height of 40 feet with an initial velocity of 64 feet per second. What is the function that models the height of the ball considering gravity?

A. ( f(x) = -32x² + 64x + 40 )
B. ( f(x) = -32x² - 64x + 40 )
C. ( f(x) = -32x² + 64x - 40 )
D. ( f(x) = -32x² - 64x - 40 )

Answer 1

The function that models the height of the ball considering gravity is A) f(x) = -32x² + 64x + 40.

Step-by-step explanation:

The function that models the height of the ball considering gravity is given by:

f(x) = -32x² + 64x + 40

where f(x) represents the height of the ball in feet and x represents the time in seconds since the ball was thrown.

The function is quadratic in form, with a negative coefficient of the square term (-32x²) indicating that the ball follows a parabolic path due to gravity.

The initial height of the ball (40 feet) is represented by the constant term (40) and the initial velocity of the ball (64 feet per second) is represented by the linear term (64x).