You did do this correctly.
You say a function has no maximum. A maximum of infinity is meaningless, as the maximum defines the highest point.
for a parabola
1) state minimum and maximum
minimum is 0
maximum is ?: would it be ∞ or would i say that there is no maximum?
2) intervals of increasing/decreasing
increasing: (0, ∞)
decreasing: (-∞ , 0)