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

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

Answer 2

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`