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Transformations of Quadratic Functions

Question 15 • FL-1200330-Algebra 2 CR

Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9? Check all of the boxes that apply.

Answer
A
The vertex is (1, -9).
B
The graph opens upward.
C
The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units.
D
The graph is narrower than the graph of f(x) = x2.
E
The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

Explanation

In vertex form, f(x) = 6(x + 1)² − 9 has vertex (−1, −9), and the positive coefficient 6 means the parabola opens upward. Since |6| > 1, it is narrower than y = x². Expanding gives 6(x² + 2x + 1) − 9 = 6x² + 12x − 3, so the equivalent equation is the one in choice E.

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