(Use the graphing feature on your calculator in cases where it would make the problem faster! ) Round all answers to the nearest hundredth where not otherwise noted.

1. (Multiple Choice) An over zealous golfer hits a flop shot with a sand wedge to get out of the corner of a

sand trip with an initial vertical velocity of 45 feet per second. What is the maximum height that the golf

ball will reach?

a. 45 feet

b. 1.41 feet

c. 31.64 feet

d. 95.36 feet

2. You sneak a slurpee onto the Giant Drop at Great America. You get nervous at the very top and when you look down you drop the slurpee. It takes about 4.9 seconds to hit the ground below. How tall is the Giant Drop?

3. After the semester is over, you discover that the math department has changed textbooks (again) so

the bookstore won't buy back your nearly-new book. You and your friend Herman decide to get creative.

You go to the roof of a twelve-story building and look over the edge to the reflecting pool 160 feet below.

You drop your book over the edge at the same instant that Herman chucks his book straight down at

48 feet per second. By how many seconds does his book beat yours into the water?

4. An athlete hits a tennis ball at an initial height of 8 feet with an initial vertical velocity of 43 ft

s.

a. After how many seconds does the ball hit the ground? b. What is the maximum height the ball will reach? c. At what time(s) will the ball to reach a height of 20 feet.

5. A rocket is shot vertically from a platform 2 feet above the ground. It reaches a maximum height of

266.02 feet after about 4.1 seconds. (If air resistance is neglected, a quadratic model provides a good

approximation for the flight of a projectile.)

a) Find the initial velocity of the rocket.

b) Find the equation that represents the distance the rocket is above the ground.

c) At what time will the rocket be 100 feet above ground?

6. An elementary wants to create a new fenced in play area. One for grades 1-3 and the

other for grades 3-5 The principal has 240 ft of fencing and plans to use all of it to create 2

identical adjacent playground areas with the part of the long side of the school as a border and a common

fence between the two.

a. Draw a diagram that represents the situation: b. What is the maximum area?

c. What are the dimensions of the playground that d. What is the domain? maximize the area.

7. The Mackinac bridge is the fifth longest suspension bridge in the world and is located in Michigan.

There is a large cable suspended between two towers that are 3800 feet apart. The cable forms a

parabola that is 52 feet above the roadbed at its lowest point and connected to the towers at 552 feet

above the roadbed. (Assume the bridge is symmetric and the roadbed is flat)

a. Write an equation that represents the vertical distance from the roadbed to the suspension cable in

terms of x. (Round your a value to 7 decimal places )

b. If you start driving across the bridge, and are 500 feet away from the first tower, how high is the

suspension cable above you?

8. A cross country Euro-train must pass through a parabolic tunnel that is 18 feet high (at its highest

point) and 24 feet across at the base.

a. Write an equation that represents the height of the

tunnel

b. Can a train that is 10 feet wide and 14 c. What is the widest 14 ft high train

tall pass through the tunnel? that can pass through the arch?

9. You started manufacturing an awesome new skateboard that all the kids are going to be asking for.

You determine the equation for the demand of your product to be 400,000 4200D P where P is the

price of your skateboard.

a. Write an equation to express the revenue R in terms of the price P.

b. At what price(s) will you bring in no money?

c. At what price should you sell your skateboards in order to maximize your revenue and what is the

maximum revenue?

10. The fence at Wrigley Field stands 15.92 feet high at the left field foul line, and is 355

feet away from home plate. When a batter hits a fly ball down the left field foul line, the

path of the baseball can be modeled by the equation 2( ) 0.003 1.11 3h x x x where

x is the horizontal distance from home plate and h is the height of the ball.

(a) Did the batter hit a homerun?

(b) How far from home plate did the ball land?

(c) What was the baseball’s maximum height?

11. On Halloween, you dropped a pumpkin from a rooftop that is 200 ft high. It took 3.54 seconds to hit

the ground. Your friend was inside the building looking out of a window that was 100 feet high. The

pumpkin passes by the window 2.5 seconds after you dropped it. Write the quadratic equation that

represents the height of the pumpkin at any time.