Lesson 9.3 WS Determine if the graph is a minimum or a maximum after identifying the a. \( \begin{array}{ll}\text { 1) } y=-2(x+4)^{2}-4 & \text { 2) } y=3(x+1)^{2}+1\end{array} \)

In these equations, the coefficient \( a \) plays a crucial role in determining whether a parabola opens upwards or downwards. For the first equation \( y = -2(x+4)^{2} - 4 \), the coefficient \( a = -2 \) is negative, indicating the parabola opens downwards, which means it has a maximum point. Conversely, in the second equation \( y = 3(x+1)^{2} + 1 \), the coefficient \( a = 3 \) is positive; hence, the parabola opens upwards, signifying a minimum point. When graphing these functions, remember to plot the vertex, which represents the maximum or minimum value. For \( y = -2(x+4)^{2} - 4 \), the vertex is at the point \((-4, -4)\) - that's your maximum! Meanwhile, for \( y = 3(x+1)^{2} + 1\), the vertex at \((-1, 1)\) represents the minimum. Just remember: if \( a \) is positive, it opens up and you have a minimum; if \( a \) is negative, it opens down and you obtain a maximum!