Question

Rewrite the following, 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.

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

Corrected quadratic in the form ax^2 + bx + c (with t as the variable):
y = -16t^2 + 32t + 0

Coefficients:
- a = -16 (half of gravity in ft/s^2, so acceleration term is -16t^2)
- b = 32 (initial upward velocity in ft/s)
- c = 0 (the constant — the initial height; here the ball is kicked from the ground)

Solve y = 0 to find landing time:
-16t^2 + 32t + 0 = 0
-16t(t - 2) = 0 → t = 0 (launch) or t = 2 seconds (landing)

So the ball returns to the ground after 2 seconds. The constant c = 0 represents the starting height (initial value).