What transformations change the graph of f(x) to the graph of g(x)?

f(x)=x squared; g(x)=(x+7)squared +9

remember

f(x-h) shifts right by h

so, you have shifted left by 7, then up by 9

the vertex of the parabola is moved from the origin (0,0) , to (-7,9)

To determine what transformations change the graph of f(x) = x^2 to the graph of g(x) = (x + 7)^2 + 9, we can compare the two functions and identify the changes.

1. Horizontal translation:
The term "x + 7" in g(x) means that the graph has shifted 7 units to the left compared to f(x). This is a horizontal translation.

2. Vertical translation:
The "+9" at the end of g(x) means that the graph has shifted upward by 9 units compared to f(x). This is a vertical translation.

3. Squaring:
Both f(x) and g(x) are squared functions, so the transformation of squaring remains the same.

In summary, the graph of g(x) includes a horizontal translation to the left by 7 units, a vertical translation upward by 9 units, and the same squaring transformation as f(x).