⦁what are the key aspects of any parabola? what do the key aspects tell you about the graph?

One form of the equation of a vertical parabola is y = x^2, which is the same as y-0 = a(x-0)^2.

If the coefficient a is positive, the parabola opens up.   If a is - the parabola opens down.

The vertex of this parabola is (0,0).  

More generally, y - k = a(x - h)^2 represents a vertical parabola that opens up if a is + and opens down if a is - and has its vertex at (h,k).

Often a = 1.  If a is greater than 1, the graph of the parabola is stretched vertically; if less than 1, the graph is compressed vertically (and thus appears to be flatter).

y - k = a(x - h)^2 is called the 'general vertex form' of a vertical parabola.

This is a quadratic equation.  With some algebra, we could rewrite

y - k = a(x - h)^2 in the form y = ax^2 + bx + c.

x-intercepts of this parabola, if any, can be found using the quadratic formula, involving the constant coefficients a, b and c.