It is odd all right. First of all if it is h(t), why is it written with x and no t on the right? The whole thing is a typo.
The -x^2 term means it will sink, not rise, as x gets large. That is why your average speed comes out negative.
4 x^2 -3 x + 2
8 x^2 + 5 x -11
as x gets big, the x^2 terms are much bigger than the terms in x and the constants so
------ = 1/2
2^2x - 4 (2^x) + 3 = 0
The trick is to see that:
2^2x = (2^x)^2
so say y = 2^x
and we have
y^2 - 4 y +3 = 0
y = 3 or y = 1
so 2^x = 3 or 2^x = 1
x log 2 = log 3 or x log 2 = log 1
x =.477/.301 or x = 0
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