Question

How do you sketch the graph of `y=x^2-5` and describe the transformation?

Answer 1

See graph and explaination

Explanation:

`y=x^2`graph{x^2 [-10, 10, -5, 5]}

Let's first look at the graph `y=x^2`
If you have a graphing calculator then plot this and then go to the table of values.

`y=x^2-5` graph{x^2-5 [-10, 10, -5, 5]}
Now lets look at `y=x^2-5`. To describe the transformation going on we can see that the function can been shifted down (or translated) down `5` units but how exactly do we know this?

Well, graphically speaking we can see this going on if we take the point `(0,0)` from `y=x^2` and see where it's located in the function `y^2-5`. We find that its now at `(0,-5)` so we say that the graph has been translated down `5` units.

Algebraically, if the above is true for the point `(0,0)` then it must be true for all points on the graph `y-x^2`.

Thus, we translate (or shift) down `5` units for every point on the graph `y=x^2` (Note: We are changing the `y` value for each point so `(0,0)` on `y=x^2` is now `(0,-5)` on `y=x^2-5` NOT #(-5,-5).

I hope this explanation proved to be very helpful and good luck! ;)