Question

Rewrite in 4 sentences in a 6th graders response.

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 = O (the constant — the initial height; since the ball is kicked from the ground, the initial height is O)
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).

Answer 1

I kicked a soccer ball straight up with an initial speed of 32 ft/s, so the height after t seconds is y = -16t^2 + 32t + 0. In this equation a = -16 (because gravity pulls it down), b = 32 (the initial speed), and c = 0 (I kicked it from the ground). To find when it lands we set -16t^2 + 32t = 0 and factor it as t(−16t + 32) = 0. That gives t = 0 (when I kicked it) or t = 2 seconds (when it comes back down), so the ball lands after 2 seconds.