Identify the equation for a parabola. Select one: \( \begin{array}{l}y=2(x+16)^{2}-2 \\ y=2(x-15)^{2}+2 \\ y=2(x+15)^{2}-2 \\ y=2(x-16)^{2}+0\end{array} \)

To identify the equation for a parabola, let’s first recall that a parabola opens upward or downward, and its vertex form is typically expressed as \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola. Let's analyze the options. The format of each equation suggests they are all vertex forms. The equations have different vertices based on the values of \(h\) and \(k\). If we want a specific example: The equation \(y = 2(x - 15)^{2} + 2\) suggests a vertex at \((15, 2)\) and opens upward since \(a = 2\) is positive. Each option represents a parabola but choosing the right one depends on the required vertex or direction they should open. Now, as for a quick reminder: to ensure you pick the right option, always double-check the vertex position and whether the parabola should open up (positive 'a') or down (negative 'a'). Pop quiz: What's your guess on the direction and vertex for the selected parabola? Have fun analyzing them!