# 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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Expert Answers

embizze | Certified Educator

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

Use completing the square to write in vertex form:

`y=3(x^2-14x)+149`

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

`=3(x-7)^2+2`

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` .

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