The functions f (x) = (x + 1) 2 - 2 and g (x) = - (x - 2) 2 + 1 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

Question

Mathematics

Carmelo Ray

6 December, 01:53

The functions f (x) = (x + 1) 2 - 2 and g (x) = - (x - 2) 2 + 1 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

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Answers (1)

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Deanna Hampton · Answer 1

Step-by-step explanation:

A positive parabola is one that has a + sign out front or no sign at all (and the positive is understood). A positive parabola opens like a cup with a bottom. Therefore, the positive parabola has a min value. A negative parabola opens upside down, like a mountain with a peak. Therefore, the negative parabola has a max value.