Question

a diver jumps from a diving - board into a pool at his swim club. his height h(t) in meters t seconds after the dive can be modeled using the equation h(t)= - 4.9t² + 4.3t + 10. what is the y - intercept for this function? what does the y - intercept represent in the given situation? the y - intercept of this function is 10. the y - intercept represents that the diver started moving 10 seconds after the time began.

Explanation:

Step1: Recall y - intercept concept

The y - intercept of a function \(h(t)=at^{2}+bt + c\) is found when \(t = 0\).

Step2: Substitute \(t = 0\) into the function

Given \(h(t)=-4.9t^{2}+4.3t + 10\), when \(t = 0\), we have \(h(0)=-4.9(0)^{2}+4.3(0)+10\).
Since \(-4.9(0)^{2}=0\) and \(4.3(0)=0\), then \(h(0)=10\).
In the context of the diving situation, the y - intercept represents the initial height of the diver. When \(t = 0\) (the start of the dive), the diver is at a height of 10 meters, which is the height of the diving board.

Answer:

The y - intercept of the function \(h(t)=-4.9t^{2}+4.3t + 10\) is 10. It represents the initial height of the diver, which is the height of the diving board (10 meters).