1. The problem is to match parabolas with their corresponding $a$-values in the quadratic function $y = ax^2 + bx + c$. 2. The value of $a$ determines the direction and steepness of the parabola: - If $a > 0$, the parabola opens upwards. - If $a < 0$, the parabola opens downwards. - The larger the absolute value of $a$, the steeper the parabola. 3. Given the graphs: - The first graph opens downwards and is steep, so $a = -4$. - The second graph opens downwards but is gentle, so $a = -0.25$. - The third graph opens upwards and is gentle, so $a = 0.25$. 4. Therefore, the matching is: - $a = -4$: steep downward parabola. - $a = -0.25$: gentle downward parabola. - $a = 0.25$: gentle upward parabola. This matches the descriptions given for each graph.