Example 2: \( g(x)=(x+4)^{2}+8 \) Vertex:

To find the vertex of the function \( g(x) = (x + 4)^{2} + 8 \), you can directly identify it from the vertex form, which is \( g(x) = a(x-h)^{2} + k \). Here, \( h \) and \( k \) represent the coordinates of the vertex. In this case, \( h = -4 \) and \( k = 8 \), so the vertex of the function is located at the point \((-4, 8)\). Vertices are crucial because they represent the highest or lowest point of a parabola. For this upward-opening parabola (since the coefficient \( a \) is positive), the vertex at \((-4, 8)\) is the minimum point. If you're plotting this function, imagine placing a point at \(-4\) on the x-axis and going up to \(8\) on the y-axis—where your parabola will beautifully curve around that point!