describing a transformation\nwhich best describes the transformation from the graph of $f(x) = x^2$ to the…

describing a transformation\nwhich best describes the transformation from the graph of $f(x) = x^2$ to the graph of $f(x) = (x - 3)^2 - 1$?\nleft 3 units, down 1 unit\nleft 3 units, up 1 unit\nright 3 units, down 1 unit\nright 3 units, up 1 unit

describing a transformation\nwhich best describes the transformation from the graph of $f(x) = x^2$ to the graph of $f(x) = (x - 3)^2 - 1$?\nleft 3 units, down 1 unit\nleft 3 units, up 1 unit\nright 3 units, down 1 unit\nright 3 units, up 1 unit

Answer

Explanation:

Step1: Identify horizontal translation

The term $(x - h)$ in $f(x) = (x - 3)^2 - 1$ indicates a horizontal shift of $h$ units. Since $h = 3$, the graph shifts right by 3 units.

Step2: Identify vertical translation

The constant $k$ in $f(x) = a(x - h)^2 + k$ indicates a vertical shift. Since $k = -1$, the graph shifts down by 1 unit.

Step3: Combine the transformations

The vertex moves from $(0, 0)$ to $(3, -1)$, which corresponds to a movement of 3 units to the right and 1 unit down.

Answer:

right 3 units, down 1 unit