Question

If Chase needs to throw a basketball so that the path of the ball follows the curve of y = -0.5x² + 5x - 8, at what point will the ball hit the ground?

A) (2, 0)
B) (5, 0)
C) (8, 0)
D) (0, 8)

Answer 1

To find the point at which the basketball hits the ground using the equation y = -0.5x² + 5x - 8, set y to 0 and solve for x. Option C is correct answer.

Step-by-step explanation:

The question involves finding the point at which a basketball, represented by its trajectory equation y = -0.5x² + 5x - 8, will hit the ground. To find this point, we need to determine the x-value when y is 0 because the ball hits the ground when its vertical position, y, is equal to 0.

To solve for x when y = 0, we set the equation equal to zero and solve for x:

0 = -0.5x² + 5x - 8

Multiplying every term by -2 to get rid of the fraction we have:

0 = x² - 10x + 16

Factoring the quadratic equation, we get:

0 = (x - 2)(x - 8)

Setting each factor equal to zero gives us x = 2 and x = 8. These are the points where the ball's path intersects the ground level. Since the ball is thrown and not dug into the ground, the point of intersection we are interested in will be the one after the ball is released, which is x = 8. Therefore, the ball will hit the ground at the point C) (8, 0).