which best describes the transformation that occurs from the graph of $f(x) = x^2$ to $g(x) = (x + 3)^2 +…

which best describes the transformation that occurs from the graph of $f(x) = x^2$ to $g(x) = (x + 3)^2 + 4$?\n\nleft 3, up 4\nright 3, down 4\nleft 3, down 4\nright 3, up 4

which best describes the transformation that occurs from the graph of $f(x) = x^2$ to $g(x) = (x + 3)^2 + 4$?\n\nleft 3, up 4\nright 3, down 4\nleft 3, down 4\nright 3, up 4

Answer

Explanation:

Step1: Identify the horizontal shift

The term $(x + 3)$ in $g(x) = (x + 3)^2 + 4$ represents a horizontal shift of $h$ units, where $x - h = x + 3$, so $h = -3$. A negative value indicates a shift to the left. $$h = -3 \text{ (left 3 units)}$$

Step2: Identify the vertical shift

The constant term $+ 4$ in $g(x) = (x + 3)^2 + 4$ represents a vertical shift of $k$ units. A positive value indicates a shift upwards. $$k = 4 \text{ (up 4 units)}$$

Step3: Combine the transformations

The graph of $f(x) = x^2$ is shifted 3 units to the left and 4 units up to obtain the graph of $g(x)$. $$\text{Transformation: left 3, up 4}$$

Answer:

left 3, up 4