Use the TI-83/4 for this one.
Below is y = x^2                                                        This graph shows y = (x – 2)^2 +3

How many spaces did it shift horizontally?
How many spaces did it shift vertically?

4x^2 – 25 is the difference of two squares as 4x^2 is a perfect square as (2x)^2 and 25 is a perfect square as 5^2.
You can find the answer by:
FOILing each of the four choices
or
Putting 4x^2 – 25 into Y1 and putting each of the others into Y2 and then either graphing to see they are the same or checking the table to see they are the same
or
Can pick a number for x like 10 and putting 10 in for x into the original expression and then into each of the choices

Domain are x values while Range are y values.

When x = 0, how much is x^2?
When x = 1, how much is x^2?
When x = 4, how much is x^2?
When x = 9, how much is x^2?