1. **Problem Statement:** We start with the base function $f(x) = -x^2$, which is a downward-opening parabola. 2. **Given Function:** We want to graph $h(x) = (x + 4)^2 + 3$ using transformations of $f(x)$. 3. **Analyze the Given Function:** Notice that $h(x)$ is a parabola opening upward because the coefficient of the squared term is positive (implicit $+1$). 4. **Compare to $f(x)$:** The base function $f(x) = -x^2$ opens downward, but $h(x)$ opens upward, so $h(x)$ is not a transformation of $f(x)$ by simple shifts or reflections alone. Instead, $h(x)$ is the standard parabola $x^2$ shifted. 5. **Transformations of $h(x)$:** - The term $(x + 4)^2$ shifts the graph of $x^2$ left by 4 units. - The $+3$ shifts the graph up by 3 units. 6. **Vertex of $h(x)$:** The vertex is at $(-4, 3)$. 7. **Graphing $h(x)$:** - Start with the graph of $f(x) = -x^2$ (downward parabola). - To graph $h(x)$, note it is a different parabola opening upward, shifted left 4 and up 3. 8. **Summary:** $h(x)$ is not a transformation of $f(x) = -x^2$ by vertical reflection or shifts alone because the sign of the squared term differs. **Final answer:** The function $h(x) = (x + 4)^2 + 3$ is an upward-opening parabola shifted left 4 units and up 3 units from the parent function $x^2$, not from $f(x) = -x^2$.