Question

question 2. a competitive diver dives from a platform into the water. the graph shown gives the height above the water y, in meters, of the diver x seconds after diving from the platform. what is the best interpretation of the x-intercept of the graph? a. the diver reaches a maximum height above the water at 1.6 seconds. b. the diver hits the water at 1.6 seconds. c. the diver reaches a maximum height above the water at 0.2 seconds. d. the diver hits the water at 0.2 seconds.

Explanation:

Step1: Recall x - intercept definition

The x - intercept of a graph is the point where \(y = 0\). In this context, \(y\) represents the height above the water (in meters) and \(x\) represents time (in seconds). So when \(y = 0\), the height above the water is 0, which means the diver is in the water.

Step2: Analyze each option

• Option A: The maximum height occurs at the vertex of the parabola - shaped graph (the peak), not at the x - intercept. So A is incorrect.
• Option B: At the x - intercept, \(y = 0\) (height above water is 0), which means the diver hits the water. From the graph, the x - intercept is around \(x = 1.6\) seconds. So this option is consistent with the meaning of the x - intercept.
• Option C: The maximum height is at the vertex (the highest point of the graph), not at the x - intercept, and the time for maximum height is not 0.2 seconds. So C is incorrect.
• Option D: The x - intercept is not at 0.2 seconds (0.2 seconds is near the vertex, the maximum height time), so D is incorrect.

Answer:

B. The diver hits the water at 1.6 seconds.