1. Problem: Describe the transformations applied to the parent function $y = x^2$ to obtain $y = -2(x + 3)^2 + 5$. 2. The parent function is $y = x^2$. The given function is $y = -2(x + 3)^2 + 5$. 3. Transformations include: - Horizontal shift left by 3 units (due to $x + 3$ inside the square). - Vertical stretch by a factor of 2 (coefficient 2). - Reflection across the x-axis (negative sign in front). - Vertical shift up by 5 units. 4. Step-by-step: - Start with $y = x^2$. - Replace $x$ by $x + 3$ to shift left: $y = (x + 3)^2$. - Multiply by $-2$: $y = -2(x + 3)^2$ (reflect and stretch). - Add 5: $y = -2(x + 3)^2 + 5$ (shift up). Final answer: The function is the parent $y = x^2$ shifted left 3 units, vertically stretched by 2, reflected over the x-axis, and shifted up 5 units.