Thread: How to determine the opening of the parabola in quadratic functions?

and also how to determine the range of it.

The general answer is too long to post. Post an example.

Write the equation in vertex form.

y = a (x - b)^2 + c

If a is negative then it opens down, otherwise it opens up.
The vertex will be at (b, c)
If it opens up then c is the lowest value in the range. If it opens down then c is the highest value in the range. The range will be either [c, ?) or (?, c] depending on which way it opens.