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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:

Step-by-step explanation:

a. The vertex is (1, -9).  False.  The vertex is (-1, -9).

b. The graph opens upward.  True.  That 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's DOWN 9 units.

d. The graph is steeper than the graph of f(x) = x^2.  True.  The given function increases 6 times faster than does x^2.

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

Let's put f(x) = 6(x + 1)^2 -9 into standard form.  Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9.  YES, TRUE

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