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

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 $\left(0 , 0\right)$ from $y = {x}^{2}$ and see where it's located in the function ${y}^{2} - 5$. We find that its now at $\left(0 , - 5\right)$ so we say that the graph has been translated down $5$ units.

Algebraically, if the above is true for the point $\left(0 , 0\right)$ 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 $\left(0 , 0\right)$ on $y = {x}^{2}$ is now $\left(0 , - 5\right)$ on $y = {x}^{2} - 5$ NOT #(-5,-5).

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