A rock is thrown upward at a speed of 85 ft/sec from the top of a 100-foot-high cliff overlooking the ocean. The rock's height above the ocean can be modeled by the function f(x)=−16x2+85x+100 where f(x) represents the height of the rock as a function of time, x. Match each question below with the characteristic of the function that is necessary to answer it. (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

Question

A rock is thrown upward at a speed of 85 ft/sec from the top of a 100-foot-high cliff overlooking the ocean. The rock's height above the ocean can be modeled by the function f(x)=−16x2+85x+100 where f(x) represents the height of the rock as a function of time, x. Match each question below with the characteristic of the function that is necessary to answer it. (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

After how many seconds would the rock hit the ocean?
After how many seconds does the rock reach its maximum height?
What is the maximum height of the rock?

word bank
the x intercept
the x value of the maximum
thr y value of maximum

Answer 1

After how many seconds would the rock hit the ocean? - the x intercept

After how many seconds does the rock reach its maximum height? - the x value of the maximum
What is the maximum height of the rock? - the y value of maximum

Answer 2

After how many seconds would the rock hit the ocean? - the x intercept

After how many seconds does the rock reach its maximum height? - the x value of the maximum

What is the maximum height of the rock? - the y value of maximum

Answer 3

To answer each question, we need to identify the specific characteristics of the function f(x) = -16x^2 + 85x + 100.

1. After how many seconds would the rock hit the ocean?
To find when the rock hits the ocean, we need to determine the time at which the height (f(x)) of the rock is zero. This corresponds to finding the x-intercept(s) of the function. So, the necessary characteristic of the function is the x-intercept.

2. After how many seconds does the rock reach its maximum height?
To determine when the rock reaches its maximum height, we need to find the x-value at which the function reaches its maximum point. This means finding the vertex of the parabolic function. So, the necessary characteristic of the function is the x-value of the maximum.

3. What is the maximum height of the rock?
To calculate the maximum height of the rock, we need to find the y-value at the vertex, which represents the highest point on the graph. This means finding the maximum value of the function. So, the necessary characteristic of the function is the y-value of the maximum.

Now, you can match the questions with the corresponding characteristics:
- After how many seconds would the rock hit the ocean? (the x-intercept)
- After how many seconds does the rock reach its maximum height? (the x value of the maximum)
- What is the maximum height of the rock? (the y value of the maximum)