Graph the following function using transformation. be sure to graph all of the stages on one graph. state domain and range. y=3x^2-42x+149

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embizze eNotes educator| Certified Educator

Graph `y=3x^2-42x+149` :

Use completing the square to write in vertex form:


   `=3(x^2-14x+49)+149-147` we added 3(49), and subtracted 3(49)


This is a parabola with the vertex at (7,2).

With the base function of `y=x^2` you transformed the base function by translating 7 units right, 2 units up, and vertically stretching by a factor of 3.


The graph: horizontal translation blue, vertical translation green, vertical stretch (and final graph) red, base function in black:

The domain is all reals, the range is `y>=2` .