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

6 meters
6 meters

0 meters
0 meters

4 meters
4 meters

2 meters

Answer 1

Vertex form: y = a(x − 4)^2 + 2. Use (0, −6): −6 = a(16) + 2 ⇒ a = −1/2. So y = −1/2(x − 4)^2 + 2. Set y = 0 (ground level) ⇒ (x − 4)^2 = 4 ⇒ x = 2 or 6. The ball was kicked at the smaller x (the starting point), so the goalkeeper was 2 meters from the goalpost. Answer: 2 meters.