Question

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by h(x) = - (x + 1)(x - 7). What was the ball's starting height?

a) 8 meters
b) 7 meters
c) 6 meters
d) 5 meters

Answer 1

The starting height of the ball, as given by the function h(x) = - (x + 1)(x - 7), is determined by evaluating the function at x = 0. Doing so, we find that the ball's initial height is 7 meters above the ground.

Step-by-step explanation:

The student wants to determine the ball's starting height from the quadratic height function h(x) = - (x + 1)(x - 7). Looking at the function, we see that it's a parabolic equation in the form of h(x) = ax^2 + bx + c. The starting height of the ball can be found by evaluating the function at x = 0, which gives us the c value in the parabolic function. This corresponds to the y-intercept of the graph of h(x).

Plugging x = 0 into the equation h(0) = - (0 + 1)(0 - 7) simplifies to h(0) = - (1)(-7), which will give us the starting height. After solving, we see that the ball's starting height is 7 meters, which corresponds to answer option b.