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)

0 meters

2 meters

4 meters

6 meters

Answer 1

Use vertex form y = a(x − 4)^2 + 2.
Plugging (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 goalkeeper is near the goalpost, so the kick was at x = 2 meters.

Answer: 2 meters.