Question

Amanda is standing 30 ft from a volleyball net. The net is 8 ft high. She serves the ball, and the path of the ball is modeled by the equation (y = -0.02(x - 18)^2 + 12), where (x) is the ball's horizontal position.

What is the vertex of the parabolic path of the ball described by the equation (y = -0.02(x - 18)^2 + 12)?
a) (18, 12)
b) (12, 18)
c) (18, -12)
d) (-18, 12)

Answer 1

The vertex of the parabolic path of the ball described by the equation y = -0.02(x - 18)^2 + 12 is (18, 12).

Step-by-step explanation:

The equation describing the path of the ball is y = -0.02(x - 18)^2 + 12. This equation is in the form y = ax + bx^2, which represents a parabola.

The vertex of the parabolic path can be found by identifying the values of x and y that minimize or maximize the equation.

In this case, the vertex occurs when x = 18. Plugging this value into the equation, we can find the corresponding y value: y = -0.02(18 - 18)^2 + 12 = 12.

Therefore, the vertex of the parabolic path of the ball is (18, 12). Option a) (18, 12) is the correct answer.