Answer:
Part a) The height of the ball after 3 seconds is
Part b) The maximum height is 66 ft
Part c) The ball hit the ground for t=4 sec
Part d) The domain of the function that makes sense is the interval
[0,4]
Step-by-step explanation:
we have
Part a) What is the height of the ball after 3 seconds?
For t=3 sec
Substitute in the function and solve for h
Part b) What is the maximum height of the ball? Round to the nearest foot.
we know that
The maximum height of the ball is the vertex of the quadratic equation
so
Convert the function into a vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point (1.97,66.02)
therefore
The maximum height is 66 ft
Part c) When will the ball hit the ground?
we know that
The ball hit the ground when h(t)=0 (the x-intercepts of the function)
so
For h(t)=0
using a graphing tool
The solution is t=4 sec
see the attached figure
Part d) What domain makes sense for the function?
The domain of the function that makes sense is the interval
[0,4]
All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds
Remember that the time can not be a negative number
