Question

F(x)=x^2 g(x) = (x– 9)^2 +3 We can think of g as a translated (shifted) version of f.

Answer 1

Answer:

To get the function g, shift f up by 3 units and to the right by 9 units.

Step-by-step explanation:

The given functions are

$f(x)=x^2$

$g(x)=(x-9)^2+3$

If f(x) is a parent function, then g(x) can be written in the form of f(x) as

$g(x)=f(x-9)+3$        ...(1)

The translation is defined as

$g(x)=f(x+a)2+b$       ... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

$a=-9,b=3$

It means, to get the function g, shift f up by 3 units and to the right by 9 units.