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.

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 steeper than the graph of f(x) = x².

E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.

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Answer:

B, D, E

Step-by-step explanation:

A. The vertex is (1, -9).

False.  The vertex is at (-1, -9).

B. The graph opens upward.

True.  The leading coefficient 6 is positive.

C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)² up 9 units.

False.  It is shifted down 9 units.

D. The graph is steeper than the graph of f(x) = x².

True.  The absolute value of the leading coefficient |6| is greater than 1.

E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.

f(x) = 6(x² + 2x + 1) - 9

f(x) = 6x² + 12x + 6 - 9

f(x) = 6x² + 12x - 3

True.