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Which statement describes the effect on the parabola f(x) = 242 - 5x + 3 when it is changed to f(x) = 212 - 5x + 1?

A. The parabola is translated up 1 unit.
B. The parabola is translated up 2 units.
C. The parabola is translated down 1 unit.
D. The parabola is translated down 2 units.

1 Answer

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Final answer:

The constant term in the quadratic function decreases from 3 to 1, which means the parabola is translated down by 2 units in response to this change.

Step-by-step explanation:

The original parabola described by the function f(x) = 242 - 5x + 3 is modified to f(x) = 212 - 5x + 1. To ascertain how this alteration affects the parabola, we need to look at the constant term in the function. The constant term, which affects the vertical translation of a parabola, has decreased from 3 to 1. This indicates a vertical shift downwards of 2 units, as the difference between the original constant term (3) and the new constant term (1) is 2. This is because the constant term in a quadratic function corresponds to the y-intercept of the graph, and decreasing the constant term results in the graph shifting downward. Therefore, the correct description of the effect on the parabola is that it is translated down 2 units.

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