Final answer:
The given equation represents the height of a ball above the ground at time t seconds. The coefficient of t² in the equation is -8, indicating that the ball is thrown upwards. The initial height of the ball is 3 feet. The ball is dropped, not thrown. The ball reaches the ground after 3 seconds. The coefficient of t² in the equation is -8, representing the acceleration due to gravity.
Step-by-step explanation:
The given equation represents the height of a ball above the ground at time t seconds. The equation is s(t) = -8t² - 4t + 3.
A) The ball is thrown upwards. The coefficient of t² in the equation is -8, which is negative, indicating that the ball is thrown upwards and then falls back down.
B) The initial height of the ball is 3 feet. When t = 0, the equation becomes s(0) = -8(0)² - 4(0) + 3 = 3, which represents the initial height of the ball.
C) The ball is dropped, not thrown. Since the coefficient of t² is negative, the ball is dropped from a higher position, rather than being thrown upwards.
D) The ball reaches the ground after 3 seconds. To find the time when the ball reaches the ground, we need to solve the equation s(t) = 0. By factoring or using the quadratic formula, we can find that the roots of the equation are t = -5.0 s and t = 4.0 s. Since time cannot be negative in this context, the ball reaches the ground after 3 seconds.
E) The coefficient of t² in the equation is -8. This represents the acceleration due to gravity, which is 9.8 m/s². Since the acceleration is negative in this case, the coefficient is -8 to represent the direction of the acceleration.