What is the range of the graph of y = 3(x – 3)^2 + 4?

Question

zepdrix · Answer

This function represents a Parabola in standard form.
A parabola, OPENING UPWARD, looks like this,$$\huge y=x^2$$Our function has been stretched by a factor of 3,$$\huge y=3x^2$$It has had it's vertex shifted to the RIGHT 3 units,$$\huge y=3(x-3)^2$$And the vertex has also been shifted UP 4 units,$$\huge y=3(x-3)^2+4$$So that's where all of those numbers are coming from.

Remember what a parabola looks like? It's like a bowl shape, in this case it's opening upward with it's lowest point at (3,4).

zepdrix · Answer

The range represents the possible Y values.
So if 4 is our LOWEST possible Y value, and it takes on every Y value larger than that, how could we write that in interval notaion? or whatever notation you're using in class :)

anonymous · Answer

y less than or equal to  4

 y greater than or equal to 4

 y  less than or equal to 3

 y greater than or equal to  3

zepdrix · Answer

The lowest point of this parabola is at (3,4).

So it's defined for all values larger than the Y value of that coordinate pair.

zepdrix · Answer

Lol, if you can't figure it out from all that info, you need to do some more homework... :CC

anonymous · Answer

Thanks I Understand now had to reread :D