Question

Use the image to answer the question.

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 2 to 10 in increments of 1. The y-axis ranges from negative 8 to 3 in increments of 1.
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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)

2 meters

4 meters

0 meters

6 meters

Answer 1

The ball is on the ground where y = 0. From the graph (or using y = a(x−4)^2 + 2 with a = −1/2), the x-intercepts are x = 2 and x = 6. The goalkeeper kicked the ball from the side near the goal, so his distance was 2 meters.

Answer: 2 meters