Question

Jane tosses a pebble upward while standing near the edge of a cliff. The function h(t) = -16t^2 + 45t + 125 represents the height of the pebble, h(t), measured in feet (t) seconds after the pebble left her hand.

A. By simply analyzing the function, determine the y-intercept of the graph of h(t).
B. Interpret what the y-intercept means in the context of the given situation.
Option 1: The y-intercept is 125 feet.
Option 2: The y-intercept is 45 feet.
Option 3: The y-intercept is -16 feet.
Option 4: The y-intercept is 0 feet.

Answer 1

The y-intercept of the function h(t) representing the height of a pebble tossed upward is the constant term 125 feet, indicating the initial height of the pebble above ground level, which in this case is the height of the cliff. Thus, Option 1 is correct: The y-intercept is 125 feet.

Step-by-step explanation:

Jane tosses a pebble upward while standing near the edge of a cliff. The y-intercept of the function h(t) = -16t^2 + 45t + 125, representing the height of the pebble in feet, t seconds after it left her hand, can be determined by looking at the constant term of the quadratic equation. The y-intercept is the value of h(t) when t = 0, which is the constant term of the function. Therefore, the y-intercept of the graph of h(t) is the constant term 125 feet. This means that when t = 0, the initial height of the pebble above the ground is 125 feet, indicating that Jane was standing on a cliff that was 125 feet high when she tossed the pebble upwards. Thus, Option 1 is correct: The y-intercept is 125 feet.