A parabola has a vertex at (-1, 2) and is symmetric about the vertical line x = -1. If it passes through the point (0, 5), write the equation of the parabola.

The vertex form of a parabola is given by the equation \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Since the vertex is at \((-1, 2)\), we have: \[ y = a(x + 1)^2 + 2 \] Now, we know the parabola passes through the point \((0, 5)\). Plugging in this point to find \(a\): \[ 5 = a(0 + 1)^2 + 2 \] This simplifies to: \[ 5 = a(1)^2 + 2 \] \[ 5 = a + 2 \] \[ a = 3 \] Thus, the equation of the parabola is: \[ y = 3(x + 1)^2 + 2 \]