Let f(x)= 3(x + 1)^2 - 12 and g(x)=x^2. Find the transformations involved to change g(x) to f(x).

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x)= 3(x + 1)^2 - 12 is obtained by the transformation of the function g(x)=x^2.

The graph of g(x) is translated -1 units in the x-direction or a translation of `((-1),(0))`. It is also translated -12 units in the in the y-direction. The translation is `((0), (-12))` . There is also a stretch parallel to the y-axis by a scale factor 3.

The function g(x) is translated by `((-1),(-12))` and stretched parallel to the y-axis by a scale factor 3 to arrive at f(x).

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