1. The problem is to match each quadratic function to its corresponding graph based on vertex, direction, and intercepts. 2. Recall the general form of a quadratic function: $$f(x) = ax^2 + bx + c$$ where the parabola opens upward if $a > 0$ and downward if $a < 0$. 3. Analyze each function: - $f(x) = -x^2 - 1$: opens downward ($a = -1$), vertex at $(0, -1)$ (since no $x$ term, vertex is at $x=0$), symmetric about $x=0$. - $g(x) = -2x^2 - 18x - 36 = -2(x + 6)(x + 3)$: opens downward ($a = -2$), roots at $x = -6$ and $x = -3$, vertex midway between roots at $x = -4.5$, vertex $y$-value can be found by substituting $x = -4.5$. - $h(x) = x^2 + 5$: opens upward ($a = 1$), vertex at $(0, 5)$, symmetric about $x=0$. - $k(x) = x^2 + 14x + 48 = (x + 8)(x + 6)$: opens upward ($a = 1$), roots at $x = -8$ and $x = -6$, vertex midway at $x = -7$. 4. Match with graphs: - Top-left: downward-opening parabola, vertex approx $(-4.5, 4.5)$, roots near $-6$ and $-3$ matches $g(x)$. - Top-right: upward-opening parabola, vertex approx $(-7, -1)$, roots near $-8$ and $-6$ matches $k(x)$. - Bottom-left: downward-opening parabola, vertex approx $(0, -1)$, symmetric about $x=0$ matches $f(x)$. - Bottom-right: upward-opening parabola, vertex approx $(0, 5)$, symmetric about $x=0$ matches $h(x)$. Final matches: - $f(x)$: bottom-left - $g(x)$: top-left - $h(x)$: bottom-right - $k(x)$: top-right