Question

a beachgoer is observing the ocean from afar. they observe a bird diving into the water to get a fish and a dolphin jumping out of the ocean. let ( d(x) ) define the path of the dolphin and ( b(x) ) define the path of the bird. use the graphs and table shown above to explore and define various key features of parabolas.

1. the ( x )-intercepts (or zeros) of a function are the point(s) where the function crosses or touches the ( x )-axis, or where ( y = 0 ). the ( x )-intercepts of ( b(x) ) are ( (1,0) ) and ( (5,0) ). this means that the height of the bird above sea level was 0 meters after 1 second and 5 seconds. what are the ( x )-intercepts of ( d(x) ) and what do these points mean in context?

Explanation:

Step1: Identify x - intercepts

The x - intercepts occur where \(y = D(x)=0\). Looking at the table for \(D(x)\), when \(D(x) = 0\), \(x = 2\) and \(x = 6\).

Step2: Interpret in context

Since \(D(x)\) defines the path of the dolphin, \(x\) represents time (in seconds) and \(D(x)\) represents the height of the dolphin above sea level (in meters).

Answer:

The x - intercepts of \(D(x)\) are \((2,0)\) and \((6,0)\). In context, this means that the height of the dolphin above sea level was \(0\) meters after \(2\) seconds and \(6\) seconds.