HI! This is from the collegeboard Digital SAT sample questions
g(x) = x2 + 55
What is the minimum value of the given function?
A) 3,025
B) 110
C) 55
D) 0
Why is the answer 55?

First, because you always have the desmos calculator available to you on the digital SAT, you can just graph this. You’ll just have to zoom out few clicks to see the parabola.

Without even clicking on the graph you can tell that the only answer choice that’s close to that minimum is 55.

BUT you didn’t ask how to use the calculator–you asked WHY the answer is 55. And there are a couple ways to approach that, but my favorite way is to incorporate function translation.

Imagine the very simple function . You can probably picture that in your mind’s eye without me including a picture but what the heck, here one is anyway.

The basic parabola has its minimum at the origin.

Now remember what happens to the graph of a function when you add or subtract a constant to the function. What would the graph of (aka ) look like? Well, each value of the function increases by 1! So the graph should look exactly the same, only one unit higher. Instead of a minimum at the origin, (0, 0), will have a minimum at (0, 1). Like so.

The reason the answer to this question is 55 is simply because we’re starting with the standard parabola and adding 55 to it.

Does that help?