The functions f (x) = (x + 1) 2 - 2 and g (x) = - (x - 2) 2 + 1 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

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Flores

Mathematics

1 May, 03:51

The functions f (x) = (x + 1) 2 - 2 and g (x) = - (x - 2) 2 + 1 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

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Alaina Gill · Answer 1

For quadratics written in the form a (x-h) ² + k:

- k is the vertex (min/max)

- It is a minimum if a is positive.

- It is a maximum if a is negative.

For our first equation, f (x) = (x+1) ² - 2, the vertex is a minimum.

(Nothing is being multiplied outside our parentheses so assumedly a = 1)

For our second, g (x) = - (x-2) ² + 1, the vertex is a maximum.

(The negative sign + the above reasoning means a = - 1 here)