what is the answer to: h(t)=4.9t²+9.8t+1

Question

A baseball player swings and hits a pop fly straight up in the air to the catcher.  The height of the baseball in meters t. seconds after it is hit is given by the quadratic function  h(t)=4.9t²+9.8t+1.  How long does it take for the baseball to reach it's maximum height?  What is the maximum height obtained by the baseball?

Answer 1

h(t)=4.9t²+9.8t+1=4.9(t²+2t)+1,

h(t)=4.9(t²+2t+1-1)+1,

h(t)=4.9(t+1)²-4.9+1=4.9(t+1)²-3.9. At t=0 the ball is 1m high, but as time moves on the ball simply gets higher and higher without limit!

I suspect that this question has an error in it because the parabola doesn't have a maximum, but it does have a minimum.

If h(t)=-4.9t²+9.8t+1, then we have a parabola which does have a maximum.

Assuming this is correct, h(t)=4.9(-t²+2t)+1=-4.9(t²-2t+1-1)+1=-4.9(t-1)²+5.9.

At t=0 the ball is 1m high, and as time moves on the ball evntually reaches its maximum height then drops back.

After 1 second, the first term drops out and we're left with 5.9m, which is the maximum height, because after one second the square term reduces from the maximum height of 5.9m.