Function g can be thought of as a translated (shifted) version of f(x)=x^2
Write and equation for g(x)

Given:

The parent function is

We need to determine the equation for the new function g(x)

Vertical shift:

From the graph, it is obvious that the parent function is shifted 6 units upwards.

The general rule to shift the graph c units upwards is

Thus, using the rule, the vertical shift of the new function g(x) is given by

Horizontal shift:

From the graph, it is obvious that the parent function is shifted 2 units to the right.

The general rule to shift the graph c units to the right is

Thus, the horizontal shift of the new function g(x) is given by

Equation for the new function g(x):

Since, the new function is shifted 2 units to the right and 6 units upward is given by the equation,

Hence, the equation of the new function is

vbbv

step-by-step explanation: