fill in the equation for this graph.\n$y = \\sqrt3{x - ?} + \\square$

Explanation:

Step1: Identify parent function

The parent function is $y=\sqrt[3]{x}$, which has a point at $(0,0)$.

Step2: Find horizontal shift

The inflection point of the given graph is at $(-3, 3)$. For the parent function, the inflection point is $(0,0)$. To shift from $x=0$ to $x=-3$, we use $x - h = x - (-3) = x + 3$, so $h=-3$. This means the value in the green box is $-3$.

Step3: Find vertical shift

The inflection point moves from $y=0$ to $y=3$, so we add 3 to the parent function. This means the value in the gray box is $3$.

Answer:

Green box: $-3$, Gray box: $3$ The full equation is $y = \sqrt[3]{x - (-3)} + 3$ or $y = \sqrt[3]{x + 3} + 3$