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What is the function g(x) created from f(x) = x2 by moving the graph left 2 units, vertically stretching it by a factor of 3, and shifting the graph up 5 units? A) g(x) = 2(x + 3)2 + 5 B) g(x) = 3(x − 2)2 + 5 C) g(x) = 3(x + 2)2 + 5 D) g(x) = 5(x + 3)2 + 2

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Answer:

g(x) = 3(x + 2)^2 + 5       (Answer C)

Step-by-step explanation:

The parent function is f(x) = x^2.

The graph of f(x) = x^2 is that of a parabola with vertex at (0, 0) and opening up.

If we move this first graph 2 units to the left, the equation becomes

h(x) = (x + 2)^2.

If we shift this new graph 5 units up, the equation becomes

g(x) = (x + 2)^2 + 5.

Finally, if we stretch the graph of this latest function by a factor of 3, we get:

g(x) = 3(x + 2)^2 + 5       (Answer C)

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