What is f(x) = 7x2 + 42x written in vertex form?

Factor out 7 from the quadratic terms: f(x) = 7(x² + 6x). Complete the square inside the parentheses by adding and subtracting 9, since half of 6 is 3 and 3² = 9: f(x) = 7[(x + 3)² − 9] = 7(x + 3)² − 63. Therefore, the vertex form is choice D, f(x) = 7(x + 3)² − 63.

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