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

Answer: Hello there!

First, let's write the things that we know:

the domain is (-∞, ∞), which means that x can have any real value

The range is [4, ∞), which means that y ≥ 4.

We have a quadratic function, which has the general shape of y = ax^2 + b^x + c

now, you want me to explain how using this information, I can know if the graph opens up or down.

Since the range is [4, ∞), this means that the minimal value that y can take is 4, and it can grow until the infinite. If the graph opens down, it reaches numbers smaller than 4 at some point ( because the domain is (-∞, ∞), which mean that the graph goes forever)

Then the graph only can open up, and the vertex of the graph should be at y = 4

Answer 2

The range of the function indicates that the function has a vertex at y=4. The number on the left in the range notation is the lowest point, the number on the right is the highest point. Since the number on the right is ∞, the graph must open up and have a minimum at 4.

Hope this helps! :)