The vertex of the parabola y = (x - 3)² + 1 is at

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Multiple Choice

The vertex of the parabola y = (x - 3)² + 1 is at

Explanation:
A parabola in vertex form y = a(x − h)^2 + k has its vertex at (h, k). Here a = 1, h = 3, and k = 1, so the vertex is (3, 1). This form shows the graph is shifted right 3 units and up 1 unit from the basic parabola y = x^2, which has vertex at (0, 0). If you expand, y = (x − 3)^2 + 1 becomes y = x^2 − 6x + 10; the x-coordinate of the vertex is −b/(2a) = 3, and substituting x = 3 gives y = 1, confirming the vertex (3, 1).

A parabola in vertex form y = a(x − h)^2 + k has its vertex at (h, k). Here a = 1, h = 3, and k = 1, so the vertex is (3, 1). This form shows the graph is shifted right 3 units and up 1 unit from the basic parabola y = x^2, which has vertex at (0, 0). If you expand, y = (x − 3)^2 + 1 becomes y = x^2 − 6x + 10; the x-coordinate of the vertex is −b/(2a) = 3, and substituting x = 3 gives y = 1, confirming the vertex (3, 1).

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