Question

Rewrite the following SENTENCES below, and state what part of the problem the constant is (remember the format is ax^2 + bx + c. where c is the initial value, which is the constant!). add a value to represent your constant for the scenario.

SENTENCES
I kick a soccer ball straight up from the ground with an initial speed of 32 feet per second, and I want to know when it will land. The height y (in feet) after t seconds is
y + 32t, and solving y = 0 shows the ball returs to the ground after after seconds. In this function t is the time in seconds, the number 16 comes from gravity (i
would use - 16t^2 when measuring in feet), and the 32 is the ball's starting upward speed.

Answer 1

Rewritten sentence (corrected and complete):
I kick a soccer ball straight up from the ground with an initial speed of 32 ft/s. The height y (in feet) after t seconds is y = -16t^2 + 32t + 0. Solving y = 0 shows the ball returns to the ground after 2 seconds.

Parts of the quadratic ax^2 + bx + c for this scenario:
- a = -16 (comes from half the acceleration due to gravity in ft/s^2; we use -16t^2)
- b = 32 (the initial upward velocity, in ft/s)
- c = 0 (the constant — the initial height; since the ball is kicked from the ground, the initial height is 0)

Work to find when it lands:
-16t^2 + 32t + 0 = 0
t(-16t + 32) = 0 → t = 0 (launch) or -16t + 32 = 0 → t = 2 s (when it returns to the ground).