A ball is kicked upward with an initial velocity of 32 feet per second. The ball's height, h (in feet), from the ground is modeled by h= 16t^2+32t, where t is measured in seconds. How much time does the ball take to reach its highest point? What is its height at this point?

a.2 sec; 16 ft

b.1 sec; 16 ft

c.1 sec; 32 ft

d.2 sec; 48 ft

Option b.1 sec; 16 ft

Step-by-step explanation:

we have

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

step 2

Complete the square

step 3

Rewrite as perfect squares

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