Consider the functions:

f(x) = x2

g(x) = (x + 1)2 – 2

h(x) = (x + 3)2 + 4

Which statement describes the relationship between the minimums of the functions?

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x).

b The minimum of g(x) is in the fourth quadrant. The minimum of h(x) is in the first quadrant.

c The minimum of g(x) is farther right and down than the minimum of f(x) and h(x).

d The minimum of g(x) is in the second quadrant. The minimum of h(x) is in the first quadrant.

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x)

Step-by-step explanation:

To know the relation between the minima of the functions you calculate the minima by using the derivative:

to find the values of x you equal the derivative of the function to zero:

by evaluating this values of x you obtain the coordinates of the minima:

hence, the coordinates will be:

f -> (0,0)

g -> (-1,-2)

h -> (-3,4)

hence, the relation is:

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x).

step-by-step explanation:

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