Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.
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Question

Quizplus · Accepted Answer

By completing the square, we can rewrite the given quadratic function as f(x) = 2(x + 3)2 - 5. This is in the form f(x) = a(x - h)2 + k, where a = 2, h = -3, and k = -5. The vertex of the parabola is at the point (-3, -5). Therefore, the correct choice is B. To express the function in the form f(x) = a(x - h)2 + k, we need to complete the square. We have: f(x) = 3x2 - 6x + 4. To complete the square, we first factor out the 3: f(x) = 3(x2 - 2x) + 4. To find the constant term we need to add inside the parentheses, we take half of the coefficient of the x-term and square it: (2/2)2 = 1. So we add 1 inside the parentheses and compensate by subtracting 3 from the overall expression: f(x) = 3(x - 1)2 + 1. Therefore, the vertex is at (1,1).

Express the Function in the Form F(x) = A(x -