Question

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

Answer 1

Given:

The parent function is $f(x)=x^2$

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 $f(x)+c$

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

$g(x)=x^2+6$

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 $f(x-c)$

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

$g(x)=(x-2)^2$

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,

$g(x)=(x-2)^2+6$

Hence, the equation of the new function is $g(x)=(x-2)^2+6$

Answer 2

Answer: g(x) = (x+2)^2+1