Question

Function g can be thought of as a translated (shifted) version of f(x) = x2.

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Write the equation for g(2).

Answer 1

Answer: x^2-3

Step-by-step explanation: KHAN ACADEMY

Answer 2

Given:

The given parent function is
`f(x)=x^2`

We need to determine the equation of the new translated (shifted) function g(x).

Vertical stretch:

The general rule to shift the graph f(x), to shift c units upward is
`g(x)=f(x)+c`

From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.

Thus, applying the above rule, we get;

`g(x)=x^2+1`

Horizontal stretch:

The general rule to shift the graph f(x) to shift c units to the left is
`g(x)=f(x+c)`

From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.

Thus, applying the above rule, we have;

`g(x)=(x+2)^2`

Equation of the new function g(x):

From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.

Thus, we have;

`g(x)=(x+2)^2+1`

Therefore, the equation of the new function g(x) is
`g(x)=(x+2)^2+1`