which best describes the transformation that occurs from the graph of f(x)=x² to g(x)=(x + 3)²+4? left 3, up…

which best describes the transformation that occurs from the graph of f(x)=x² to g(x)=(x + 3)²+4? left 3, up 4 right 3, down 4 left 3, down 4 right 3, up 4

which best describes the transformation that occurs from the graph of f(x)=x² to g(x)=(x + 3)²+4? left 3, up 4 right 3, down 4 left 3, down 4 right 3, up 4

Answer

Explanation:

Step1: Recall transformation rules

For $y = f(x - h)+k$, $h$ is horizontal shift and $k$ is vertical shift.

Step2: Analyze horizontal shift

For $g(x)=(x + 3)^2+4$ compared to $f(x)=x^2$, we have $h=- 3$. A negative $h$ means a left - shift of 3 units.

Step3: Analyze vertical shift

Here $k = 4$. A positive $k$ means an up - shift of 4 units.

Answer:

left 3, up 4