Ajuggler tosses a ball into the air . the balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40t+4 . suppose the juggler missed and ball hit the ground . find the maximum height of the ball and time it took to reach the ground. round all answers to the nearest hundredth .

PART A

The given equation is



In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,



We add and subtract



to get,



We again factor -16 out of the first two terms to get,



This implies that,



The quadratic trinomial above is a perfect square.



This finally simplifies to,



The vertex of this function is



The y-value of the vertex is the maximum value.

Therefore the maximum value is,



PART B

When the ball hits the ground,



This implies that,



We add -29 to both sides to get,



This implies that,









or



Since time cannot be negative, we discard the negative value and pick,

$250 deductible means jane must pay the first $250 of her bill. so the insurance company paid = (80% of bill) - deductible = (0.8 x $2550) - $250 = $2040 - $250 = $1790 and jane's cost is = (bill) - (insurance payment) = $2550 - $1790 = $760