Questions: Graph the function and its parent function. Then describe the transformation. g(x) = 1/2(x+2)^2 + 3 a. The graph of g is a translation 2 units right, a vertical shrink, and a translation 3 units down of the parent quadratic function. b. The graph of g is a translation 2 units right, a vertical shrink, and a translation 3 units up of the parent quadratic function. c. The graph of g is a translation 2 units

Solution Steps

The parent function for the given quadratic function \( g(x) = \frac{1}{2}(x + 2)^2 + 3 \) is \( f(x) = x^2 \).

The given function \( g(x) = \frac{1}{2}(x + 2)^2 + 3 \) can be broken down into transformations of the parent function \( f(x) = x^2 \):

• Horizontal Translation: The term \( (x + 2) \) indicates a translation 2 units to the left.
• Vertical Stretch/Shrink: The coefficient \( \frac{1}{2} \) indicates a vertical shrink by a factor of \( \frac{1}{2} \).
• Vertical Translation: The term \( +3 \) indicates a translation 3 units up.

Combining all the transformations, the function \( g(x) = \frac{1}{2}(x + 2)^2 + 3 \) is obtained by:

1. Translating the parent function 2 units to the left.
2. Applying a vertical shrink by a factor of \( \frac{1}{2} \).
3. Translating the function 3 units up.

Final Answer