How do I graph this function?
y=4(x-9)^2+29

Question

How do I graph this function? 
y=4(x-9)^2+29

anonymous · Answer

Using graphing transformations

anonymous · Answer

What happens when you add a constant to the function?  How is the graph affected? Does it move left, right, up, down, elongate, shrink?

anonymous · Answer

It moves up?

anonymous · Answer

Yes!  So, you know at y=0 we are at x=29, so we have a parabola with vertex at (29, 0) and is facing up.  Now, what happens when you subtract something from the inside of the function e.g. (x-9)^2 what does that -9 do to the function.  If it helps think about (x-9) what happens then which way is the graph shifted

anonymous · Answer

Does it become a positive 9?

anonymous · Answer

Yes, so what does that mean for the graph? Where is it shifted

anonymous · Answer

To the right?

anonymous · Answer

exactly! So, now our vertex gets shifted over 9 and so we have (29, 9).  Now what happens when you multiply your function by an integer? 4(x-9)^2 what happens to the y-values for every x you plug in? How is the graph affected?

anonymous · Answer

I'm confused :P

anonymous · Answer

Okay, so we know this is a parabola facing upwards and it is shifted up and to the left at (29, 9) now we have to see what that 4 does to the graph so just plug in x-values and that will give you your y-values so you can graph it.  And when you do that you will notice that the 4 makes the graph either get wider or slimmer.

anonymous · Answer

So just plug any number into x and solve?

anonymous · Answer

well, you need a couple to get an idea for what the graph looks like