Question

Question was provided via image upload.

Explanation:

Identify the parent function and transformations

$$
LATEXBLOCK0
$$

Determine the geometric shifts and reflections

$$
LATEXBLOCK1
$$

Locate the transformed vertex/turning point

$$
LATEXBLOCK2
$$

Answer:

To graph the function \(h(x) = 2 - (x - 3)^4\), apply the following transformations to the parent graph \(y = x^4\):

1. Shift the graph 3 units to the right to get \(y = (x - 3)^4\).
2. Reflect the graph vertically across the \(x\)-axis to get \(y = -(x - 3)^4\).
3. Shift the graph 2 units upward to get \(h(x) = -(x - 3)^4 + 2\).

The vertex (turning point) of the graph is shifted from \((0,0)\) to \((3, 2)\), and the curve opens downward.