Vertex X Coordinate 8371F1

1. **Problem Statement:** We are given that $f(1) = f(-5)$ and want to determine if this implies the $h$ value of the vertex of the parabola is $-3$. 2. **Recall the vertex form of a quadratic function:** $$f(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. 3. **Key property:** For a parabola, if $f(1) = f(-5)$, then the points $x=1$ and $x=-5$ are symmetric about the vertex's $x$-coordinate $h$. 4. **Calculate the midpoint between $1$ and $-5$:** $$h = \frac{1 + (-5)}{2} = \frac{-4}{2} = -2$$ 5. **Conclusion:** The $h$ value of the vertex is $-2$, not $-3$. The vertex lies exactly halfway between the two $x$-values where the function has the same output. Therefore, using the fact that $f(1) = f(-5)$, we find the vertex's $x$-coordinate $h = -2$.