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

1 Answer
Anthony R.
Mar 21, 2017

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! ;)

Related questions
See all questions in Vertical Shifts of Quadratic Functions
Impact of this question
9484 views around the world
You can reuse this answer
Creative Commons License