18. a soccer ball is kicked upward from a height of 1.5 feet with an initial vertical velocity of 35 feet per second. its
height can be modeled by the quadratic function h(t) = -16t2 + 35t + 1.5 where h(t) is the height, in feet, of the
soccer ball and t is the time the ball has been in the air, in seconds.
a. write an equation that could be used to determine the time the ball traveled before it hit the ground.
b. determine the values of a, b, and c.
a=16 0 35 1=15
c. how long will it take for the soccer ball to each the ground after it was kicked? round to the nearest hundredth.

Part a)

Part b)

Part c) The soccer ball will take 2.23 seconds to reach the ground

Step-by-step explanation:

we have

where

t  is the time the ball has been in the air, in seconds

h(t) is the height, in feet, of the  soccer ball

Part a) Write an equation that could be used to determine the time the ball traveled before it hit the ground

we know that

When the ball hit the ground, the value of h(t) is equal to zero

so

For h(t)=0

This equation can be used to determine the time the ball traveled before it hit the ground

Part b) Determine the values of a, b, and c

we know that

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

Part c)  How long will it take for the soccer ball to reach the ground after it was kicked?

Solve the quadratic equation by the formula

we have

substitute the values

 ---> cannot be a solution (is negative)

therefore

The soccer ball will take 2.23 seconds to reach the ground

answer: are you

step-by-step explanation: