Question

BALLOON Trayvon is standing 9 yards from the base of a hill that has a slope of 1/5. He throws a water balloon from a height of 2 yards. Its path is modeled by h(x) = -0.1x^2 + 0.8x + 2, where h is the height of the balloon in yards, and x is the distance the balloon travels in yards.

a. Write a polynomial equation to represent the situation.

h(x) = -0.1x^2 + 0.8x + 2
h(x) = 0.1x^2 - 0.8x + 2
h(x) = 0.1x^2 + 0.8x + 2
h(x) = -0.1x^2 - 0.8x + 2

Answer 1

The correct polynomial equation for the trajectory of Trayvon's water balloon is h(x) = -0.1x^2 + 0.8x + 2, which is a quadratic function that models projectile motion.

Step-by-step explanation:

The correct polynomial equation that represents the situation where Trayvon throws a water balloon from a height of 2 yards and its path is modeled by h(x) = -0.1x2 + 0.8x + 2, is h(x) = -0.1x2 + 0.8x + 2. In physics and mathematics, this type of equation typically models the trajectory of a projectile, considering factors such as initial velocity, angle of launch, and gravitational acceleration. This specific equation is a quadratic function representing the height (h) of the balloon in yards as a function of the distance it travels (x) in yards, with the height starting at 2 yards, a linear coefficient of 0.8 (representing initial velocity component in the vertical direction), and a quadratic coefficient of -0.1 (representing the acceleration due to gravity).