Question

Jacob’s classroom is on the second floor of his high school building. He’s sitting at his desk and trying to solve a quadratic equation. Every time he makes a mistake, he crumples a piece of paper and attempts to throw it in the trash can. One time, however, he accidentally throws the ball of paper out the window. The quadratic expression -16t^2 − 8t + 24, where t is the time (in seconds), models the height (in feet) of the crumpled ball of paper after passing through the open window at t = 0.

In the expression -16t² − 8t + 24, what does the constant term represent?

a) Initial height of the paper ball
b) Initial velocity of the paper ball
c) Time the paper ball was thrown
d) Acceleration of the paper ball

Answer 1

In the quadratic equation modeling the motion of Jacob's crumpled paper ball, the constant term +24 represents the initial height of the ball above the ground at the moment it passes through the window.

Step-by-step explanation:

The quadratic equation -16t² − 8t + 24 describes the motion of the crumpled ball of paper Jacob throws out the window. In this equation, the constant term refers to the initial height of the paper ball above the ground at the time t = 0 seconds, when it passed through the window. As the standard form of a quadratic equation representing the motion of an object under gravity is at² + bt + c, where a represents acceleration due to gravity, b represents the initial vertical velocity, and c represents the initial height, we can identify that the constant term c in Jacob's equation corresponds to the initial height of the paper ball.