What is the equation of the translated function, g(x), if
f(x) = x2?

g(x) = (x – 4)2 + 6
g(x) = (x + 6)2 – 4
g(x) = (x – 6)2 – 4
g(x) = (x + 4)2 + 6

we have

the vertex is the point

The vertex of the function g(x) is

so

the rule of the translation  of f(x) to g(x) is equal to

that means

the translation  is units to the left and units up

the equation of g(x) is

therefore

the answer is

(-5,-28)

i graphed to on desmos.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have