Download Scholarship Algebra II Quadratic Word Problems Use the

Scholarship Algebra II
Quadratic Word Problems
Use the discriminant to describe the solutions (how many and what kind) for each quadratic equation below:
1.
2𝑥 2 + 4𝑥 + 3 = 0
2. 3𝑥 2 − 11𝑥 − 6 = 0
3. 4𝑥 2 − 20𝑥 + 25 = 0
4. 5𝑥 2 − 3𝑥 = 10𝑥 − 12
Answer each of the following questions. Round your answers to two decimal places when necessary.
5.
The function 𝑅 = −3𝑝2 + 150𝑝 + 1280 models the daily revenue for a company that makes scientific calculators, where R is the
revenue and p is the price per calculator.
a. What price would the company have to charge to make $1000 per day?
b. Use the discriminant to show that the company cannot make $4000 per day.
c. What is the maximum amount that they can make per day?
6.
The height of a punted football can be modeled with the function ℎ = −0.01𝑥 2 + 1.38𝑥 + 2, where h is the height of the ball (in ft) and x
is the horizontal distance (in ft).
a. The receiver is waiting 145 ft away from the punter. Use the discriminant to determine whether the ball will land in front of
him or behind him.
b. How far will the football get down the field? (AKA where will it hit the ground again?)
c. How high will the ball get in the air at its peak?
7.
An army is trying to invade a foreign city with a huge wall around it. A cannon launches a cannonball in an arc through the air modeled by
the quadratic function ℎ = 80𝑡 − 16𝑡 2 , where h is the height of the cannonball (in ft) and t is the amount of time it was in the air (in sec).
a. The wall surrounding the city is 85 ft. tall. Can the cannonball clear the wall?
b. How many seconds will it take the cannonball to hit the ground again?
8.
A man catapults a watermelon off of a building. The path that the watermelon takes is modeled by the quadratic ℎ = −4𝑠 2 + 20𝑠 + 28,
where h is the height of the watermelon (in ft) and s is the number of seconds that it has been in the air.
a. How high does the watermelon get at its highest point? How long does it take to get there?
b. How long will it take for the watermelon to hit the ground?
Scholarship Algebra II
Quadratic Word Problems
Use the discriminant to describe the solutions (how many and what kind) for each quadratic equation below:
1.
2𝑥 2 + 4𝑥 + 3 = 0
2. 3𝑥 2 − 11𝑥 − 6 = 0
3. 4𝑥 2 − 20𝑥 + 25 = 0
4. 5𝑥 2 − 3𝑥 = 10𝑥 − 12
Answer each of the following questions. Round your answers to two decimal places when necessary.
5.
The function 𝑅 = −3𝑝2 + 150𝑝 + 1280 models the daily revenue for a company that makes scientific calculators, where R is the
revenue and p is the price per calculator.
a. What price would the company have to charge to make $1000 per day?
b. Use the discriminant to show that the company cannot make $4000 per day.
c. What is the maximum amount that they can make per day?
6.
The height of a punted football can be modeled with the function ℎ = −0.01𝑥 2 + 1.38𝑥 + 2, where h is the height of the ball (in ft) and x
is the horizontal distance (in ft).
a. The receiver is waiting 145 ft away from the punter. Use the discriminant to determine whether the ball will land in front of
him or behind him.
b. How far will the football get down the field? (AKA where will it hit the ground again?)
c. How high will the ball get in the air at its peak?
7.
An army is trying to invade a foreign city with a huge wall around it. A cannon launches a cannonball in an arc through the air modeled by
the quadratic function ℎ = 80𝑡 − 16𝑡 2 , where h is the height of the cannonball (in ft) and t is the amount of time it was in the air (in sec).
a. The wall surrounding the city is 85 ft. tall. Can the cannonball clear the wall?
b. How many seconds will it take the cannonball to hit the ground again?
8.
A man catapults a watermelon off of a building. The path that the watermelon takes is modeled by the quadratic ℎ = −4𝑠 2 + 20𝑠 + 28,
where h is the height of the watermelon (in ft) and s is the number of seconds that it has been in the air.
c. How high does the watermelon get at its highest point? How long does it take to get there?
d. How long will it take for the watermelon to hit the ground?