1. The population (in thousands) for Alpha City, t years after January 1, 2004 is modeled by the quadratic function 𝑦 = 0.3𝑡 2 +
6𝑡 + 80. In what year does Alpha City’s population reach twice its initial (1/1/2004) population?
2. The population (in thousands) for Beta City, t years after January 1, 2005 is modeled by the quadratic function 𝑦 = 0.7𝑡 2 +
12𝑡 + 200. How long will it take Beta City’s population to reach 350 thousand?
3. The population (in thousands) for Gamma City, t years after January 1, 2002 is modeled by the quadratic function 𝑦 =
1.5𝑡 2 + 21𝑡 + 300. How long will it take Gamma City’s population to reach 500 thousand?
4. The population (in thousands) for Delta City, t years after January 1, 2003 is modeled by the quadratic function 𝑦 = 0.5𝑡 2 +
7𝑡 + 90. In what year does Alpha City’s population reach twice its initial (1/1/2003) population?
5. The trajectory of a soccer ball is given by the equation 𝑦 = −16𝑡 2 + 48𝑡 where t = seconds and y = feet. Find the maximum
height attained by the ball and the time it takes for the ball to return to the ground.
6. The trajectory of a baseball thrown from the top of a 56 foot building is given by the equation 𝑦 = −16𝑡 2 + 32𝑡 + 56 where
t = seconds and y = feet. Find the maximum height attained by the ball and the time it takes for the ball to hit the ground.
7. The trajectory of a tennis ball thrown straight up from a 160 feet tall building is given by the equation 𝑦 = −16𝑡 2 + 52𝑡 +
160 where t = seconds and y = feet. The ball soon falls to the ground at the base of the building. How long does the ball
remain in the air?
8. The trajectory of a golf ball dropped from a 960 feet tall building is given by the equation 𝑦 = −16𝑥 2 + 960 where t =
seconds and y = feet. How long does it take the ball to hit the ground?
9. Researchers compared protein intake to average shoulder and kidney weight for a group of pigs. Write two quadratic
regression equations, one comparing shoulder weight to protein intake and the other comparing kidney weight to protein
intake.
10. The table shows the distance, in meters, traveled by a baseball hit at various angles and with different types of spin. Write
three quadratic regression equations, one comparing backspin to angle hit, one comparing no spin to angle hit, and the other
comparing top spin to angle hit.
11. A farmer wants to use the 7200 feet of fence he has to create a new pasture for his cows. What dimensions should he use if
he wants to enclose as much land as possible?
12. A gardener has 400 linear feet of brick to partition her garden. She wants the length of the garden to be twice as long as
the width of the garden. What should the dimensions be if she wants to maximize the garden’s area?
1. The population (in thousands) for Alpha City, t years after January 1, 2004 is modeled by the quadratic function 𝑦 = 0.3𝑡 2 +
6𝑡 + 80. In what year does Alpha City’s population reach twice its initial (1/1/2004) population?
2. The population (in thousands) for Beta City, t years after January 1, 2005 is modeled by the quadratic function 𝑦 = 0.7𝑡 2 +
12𝑡 + 200. How long will it take Beta City’s population to reach 350 thousand?
3. The population (in thousands) for Gamma City, t years after January 1, 2002 is modeled by the quadratic function 𝑦 =
1.5𝑡 2 + 21𝑡 + 300. How long will it take Gamma City’s population to reach 500 thousand?
4. The population (in thousands) for Delta City, t years after January 1, 2003 is modeled by the quadratic function 𝑦 = 0.5𝑡 2 +
7𝑡 + 90. In what year does Alpha City’s population reach twice its initial (1/1/2003) population?
5. The trajectory of a soccer ball is given by the equation 𝑦 = −16𝑡 2 + 48𝑡 where t = seconds and y = feet. Find the maximum
height attained by the ball and the time it takes for the ball to return to the ground.
6. The trajectory of a baseball thrown from the top of a 56 foot building is given by the equation 𝑦 = −16𝑡 2 + 32𝑡 + 56 where
t = seconds and y = feet. Find the maximum height attained by the ball and the time it takes for the ball to hit the ground.
7. The trajectory of a tennis ball thrown straight up from a 160 feet tall building is given by the equation 𝑦 = −16𝑡 2 + 52𝑡 +
160 where t = seconds and y = feet. The ball soon falls to the ground at the base of the building. How long does the ball
remain in the air?
8. The trajectory of a golf ball dropped from a 960 feet tall building is given by the equation 𝑦 = −16𝑥 2 + 960 where t =
seconds and y = feet. How long does it take the ball to hit the ground?
9. Researchers compared protein intake to average shoulder and kidney weight for a group of pigs. Write two quadratic
regression equations, one comparing shoulder weight to protein intake and the other comparing kidney weight to protein
intake.
10. The table shows the distance, in meters, traveled by a baseball hit at various angles and with different types of spin. Write
three quadratic regression equations, one comparing backspin to angle hit, one comparing no spin to angle hit, and the other
comparing top spin to angle hit.
11. A farmer wants to use the 7200 feet of fence he has to create a new pasture for his cows. What dimensions should he use if
he wants to enclose as much land as possible?
12. A gardener has 400 linear feet of brick to partition her garden. She wants the length of the garden to be twice as long as
the width of the garden. What should the dimensions be if she wants to maximize the garden’s area?