Which of the following scenarios would use a quadratic equation to solve?

Question

A coach models the trajectory of a ball to find out how high the player is kicking the ball.
A coach models the trajectory of a ball to find out how high the player is kicking the ball.

A child places a quarter into a piggy bank every week.
A child places a quarter into a piggy bank every week.

An accountant models the growth of a savings account that doubles every month to find how much will be in the account in 10 years.
An accountant models the growth of a savings account that doubles every month to find how much will be in the account in 10 years.

The trajectory of a balloon that rises 2 feet per second is modeled to find how high the balloon will be in 5 minutes.
The trajectory of a balloon that rises 2 feet per second is modeled to find how high the balloon will be in 5 minutes.

Answer 1

Among the scenarios listed, the one that would use a quadratic equation to solve is:

A coach models the trajectory of a ball to find out how high the player is kicking the ball.

This scenario involves the motion of a projectile, which is typically described by a quadratic equation due to the parabolic trajectory caused by gravity.

The other scenarios do not involve quadratic equations:

• A child placing a quarter into a piggy bank every week describes a linear situation as the total money increases by a fixed amount weekly.
• An accountant models the growth of a savings account that doubles every month describes exponential growth, which is modeled by exponential functions rather than quadratic equations.
• The trajectory of a balloon that rises 2 feet per second describes linear motion, as the height increases at a constant rate.