Question

How can you use the vertex and the sign of "a" to determine the range and absolute value of the function?

Answer 1

you can...

if a is positive the range is greater than or equal to the y value in the vertex
( this is a minimum at the vertex)

if a is negative is will be less than or equal to the y value in the vertex
(this is a maximum at the vertex)

provided the parabola is in the form

y = ax^2 + bx + c