How does the function \( f(x)=\frac{1}{2}(x+2)^{2}-3 \) compare to the parent function? Facing down since a is less than 1 with a vertex at \( (2,-3) \) Facing up since a is greater than 1 with a vertex as \( (2,-3) \). Stretched since a is less than 1 with a vertex at \( (-2,-3) \). Compressed since a is less than one with a vertex at \( (-2,-3) \)

The function \( f(x) = \frac{1}{2}(x + 2)^2 - 3 \) can be compared to the parent quadratic function \( y = x^2 \) by analyzing its components: 1. **Vertex**: - The given function is in the vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. - Here, \( h = -2 \) and \( k = -3 \), so the vertex is at \( (-2, -3) \). 2. **Direction (Facing Up or Down)**: - The coefficient \( a = \frac{1}{2} \) is positive. - Since \( a > 0 \), the parabola **faces up**, just like the parent function. 3. **Vertical Stretching or Compression**: - The value of \( a = \frac{1}{2} \) is less than 1. - When \( |a| < 1 \), the parabola is **vertically compressed** compared to the parent function. This means it is wider and "flatter." Putting it all together, the correct description is: **Compressed since \( a \) is less than one with a vertex at \( (-2, -3) \).** **Answer:** Compressed since a is less than one with a vertex at (–2, –3).