Question

The graph of a quadratic function has a domain of (-∞, ∞) and range of [4, ∞). In two or more complete sentences, explain how the given range of the function can help you to determine whether the graph opens up or down.

Answer 1

RANGE  gives you the possible y values. [4, ∞) means the lowest y value - y coordinate of the vertex is 4 and the y is increasing from 4 upwards towards infinity. The graph opens up. 
DOMAIN gives you the possible x's. As you can see no restrictions.