Answer:
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground
Step-by-step explanation:
we have
This is a vertical parabola open downward
The vertex represent a maximum
where
t represent the time in seconds
h(t) represent the height of the ball
What is the axis of symmetry, and what does it represent?
we know that
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
Convert the quadratic equation into vertex form
step 1
Factor -16
step 2
Complete the square
step 3
Rewrite as perfect squares
The vertex is the point (3,144)
That means ----> It takes the ball 3 seconds to reach the maximum height of 144 units
The x-coordinate of the vertex is 3
therefore
The equation of the axis of symmetry is
step 4
Find how long take to the ball hit the ground
we know that
When the ball hit the ground the height is equal to zero
so
For h(t)=0
Solve for t
take square root both sides
so
therefore
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground