Answer:
Option b.1 sec; 16 ft
Step-by-step explanation:
we have
[tex]h(t)=-16t^2+32t[/tex]
where
h(t) is the ball's height in feet
t is the time in seconds
This is the equation of a vertical parabola open downward
The vertex represent a maximum
The y-coordinate of the vertex represent the highest point of the ball
Convert the quadratic equation in vertex form
step 1
Factor -16
[tex]h(t)=-16(t^2-2t)[/tex]
step 2
Complete the square
[tex]h(t)=-16(t^2-2t+1)+16[/tex]
step 3
Rewrite as perfect squares
[tex]h(t)=-16(t-1)^2+16[/tex]
The vertex is the point (1,16)
That means
The ball takes 1 second to reach its highest point
Its highest point is 16 feet
