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 ( y )-intercept of a function is the point that crosses the ( y )-axis. this is also called the initial value. the ( y )-intercept of ( d(x) ) is ( (0,-6) ). this means that the dolphin was 6 meters below sea level when the beachgoer begins watching. what is the ( y )-intercept of ( b(x) ) and what does this point mean in context?

type a response

Explanation:

Step1: Identify the y - intercept of \( B(x) \)

The y - intercept of a function \( y = f(x) \) is the value of \( y \) when \( x = 0 \). Looking at the table for \( B(x) \), when \( x = 0 \), \( B(0)=1 \).

Step2: Interpret the y - intercept in context

In the context of the bird's path (since \( B(x) \) defines the path of the bird), the point \((0,1)\) means that when the beachgoer begins watching (at \( x = 0 \), where \( x \) might represent time or some independent variable related to the observation start), the bird is 1 unit (assuming the units of the function \( B(x) \) are in meters, for example) above sea level.

Answer:

The y - intercept of \( B(x) \) is \((0,1)\). This means that the bird was 1 meter above sea level when the beachgoer begins watching.