Question

The parabola passes through coordinates left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 8 comma negative 6 right parenthesis. The vertex has coordinates left parenthesis 4 comma 2 right parenthesis.


A sports analyst graphed the trajectory of a soccer ball that was kicked by a goalkeeper. In the graph, x is the ball’s distance from the goalpost, and y is the height of the ball in meters. What was the goalkeeper’s distance from the goalpost when the ball was kicked?

(1 point)
Responses

4 meters
4 meters

6 meters
6 meters

0 meters
0 meters

2 meters

Answer 1

The parabola is y = a(x−4)^2 + 2. Using (0, −6): −6 = 16a + 2 ⇒ a = −1/2. So y = −1/2(x−4)^2 + 2. Set y = 0 to find where the ball was kicked (ground level):

0 = −1/2(x−4)^2 + 2 ⇒ (x−4)^2 = 4 ⇒ x = 2 or x = 6.

The goalkeeper kicked the ball at the closer ground point, x = 2 meters. Answer: 2 meters.