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.

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)

the vertex of f(x) is (-1,-2) and it is the minimum value of the function. the vertex of g(x) is (2,1) and it is the maximum value of the function.

step-by-step explanation:

the given functions are

the standard vertex form of a parabola is

where, a is stretch factor and (h,k) is vertex. the vertex of a parabola is an extreme point of it.

if a< 0, then it is a downward parabola and if a> 0, then it is an upward parabola.

in function f(x),

here a> 0, therefore it is an upward parabola. so, the vertex (-1,-2) is the minimum value of the function.

in function g(x),

here a< 0, therefore it is a downward parabola. so, the vertex (2,1) is the maximum value of the function.

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Step-by-step explanation:

imagine 2 cookies and you baked 0 more. how many cookies do you have now?

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