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Over what interval is the graph of y = 2 + (x - 3)^2 increasing?

A. (-3, infinite)
B. (- infinite, 3)
C. (- infinite, -3)
D. (3, infinite)

User Sytech
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1 Answer

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Final answer:

The graph of the quadratic function y = 2 + (x - 3)^2 is increasing over the interval (3, infinity) because it is a parabola that opens upwards with its vertex at (3, 2), and the function begins to increase to the right of this vertex.

Step-by-step explanation:

To determine over which interval the function y = 2 + (x - 3)^2 is increasing, we need to understand the behavior of a quadratic function. The given function is a parabola that opens upwards since the coefficient of x2 is positive. The vertex of this parabola is at (3, 2), which is also its minimum point.

Since a parabola opens upwards, the function is decreasing on the interval to the left of the vertex, and increasing on the interval to the right of the vertex. So, for x > 3, the function starts to increase, meaning the graph is increasing over the interval (3, infinity).

User Mjaskowski
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