1. The problem is to match parabolas of the form $y = ax^2 + bx + c$ with their $a$-values based on the shape and direction of their graphs. 2. Recall that the coefficient $a$ determines the parabola's opening direction and steepness: - 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 upwards and is relatively steep, so $a$ is positive and large in magnitude. - The second graph opens upwards but is less steep, so $a$ is positive but smaller in magnitude. - The third graph opens downwards and is steep, so $a$ is negative and large in magnitude. 4. Matching the given $a$-values: - $a = 4$: steep upward parabola (matches first graph). - $a = 1$: gentle upward parabola (matches second graph). - $a = -1$: steep downward parabola (matches third graph). 5. Therefore, the correct matching is: - First graph: $a = 4$ - Second graph: $a = 1$ - Third graph: $a = -1$