which best describes the transformation that occurs from the graph of f(x) = x² to g(x) = (x - 2)²+ 3? right…

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

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

Answer

Explanation:

Step1: Recall transformation rules

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

Step2: Analyze horizontal shift

In $g(x)=(x - 2)^2+3$, comparing with $y = f(x - h)+k$, $h = 2$. A positive $h$ means shift right by 2 units.

Step3: Analyze vertical shift

In $g(x)=(x - 2)^2+3$, $k = 3$. A positive $k$ means shift up by 3 units.

Answer:

right 2, up 3