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.

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.

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

details

step-by-step explanation: