# How do you graph #16(x-9)=(y+9)^2#?

##### 1 Answer

It would be a sideways parabola.

graph{x=((y+9)^2)/16+9 [-56.3, 91.86, -45.3, 28.74]}

#### Explanation:

There are two ways to interpret this relation between

- Let y be the independent variable and x be the dependent variable. Write the equation as
#y=...x# - Rewrite the equation so
#x# is the dependent variable:#x=...y# then rotate the graph so that#y# is the dependent variable again.

Option 1 is easier to understand but harder to rewrite this equation for. Option 2 takes a new approach at looking at the nature of graphs. We'll be going for Option 2.

We know that in the Cartesian plane, **"If I have #x#, I can find #y#"**.

What if we rewrite this such that **"If I have #y#, I can find #x#"**?

So, how does this relate to your question?

In

At this point, I believe that using *function notation* is easier to declare which variable is independent and which is dependent. If you are unfamiliar, this is a quick overview:

In **dependent** variable and **independent** variable.

In **dependent** and the **independent**.

Consider your equation rewritten using function notation:

And then we switch

We'll call this rewritten function

When we graph this out with the axis switched, we get a parabola as expected:

graph{y=(x+9)^2/16+9 [-122.1, 115.1, -2.4, 116.3]}

However, we must switch the roles of

graph{x=((y+9)^2)/16+9 [-56.3, 91.86, -45.3, 28.74]}

I'd like to leave off at this property:

If

And

Then