The expression is in vertex form, which makes the properties of the parabola easy to discern. The transformations entailed in g(x) are as follows:
A vertical compression by a factor of 1/3, meaning every x value gets their y value divided by 3;
A horizontal shift 6 units to the right; and
A vertical shift 1 unit up.
Thus the vertex should be (6,1) (ah_furry is correct on this).
To properly graph the points found on g(x), you have to draw a table that contains the points found on the parent function, f(x) = x². The parent function's table is as follows:
[(-3,9), (-2,4), (-1,1), (0,0), (1,1), (2,4), (3,9)]
Vertical compressions and shifts both affect the y-values, while horizontal shifts affect the x-values. Therefore, you would have to add 6 to every x-value (x + 6) and add 1 to every y-value divided by 3 (y/3 + 1).
The resulting graph should be:
[(3,4), (4,7/3), (5,4/3), (6,1), (7,4/3), (8,7/3), (9,4)]
Caption this Meme
