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.

**Step 1: Write the vertex form** The vertex form of a parabola is given by \[ y = a(x - h)^2 + k, \] where \((h, k)\) is the vertex. Given the vertex \((-1, 2)\), substitute \(h = -1\) and \(k = 2\) to obtain \[ y = a(x + 1)^2 + 2. \] **Step 2: Use the point to determine \(a\)** The parabola passes through the point \((0, 5)\). Substitute \(x = 0\) and \(y = 5\) into the equation: \[ 5 = a(0 + 1)^2 + 2. \] This simplifies to: \[ 5 = a + 2. \] Subtract 2 from both sides: \[ a = 3. \] **Step 3: Write the final equation** Substitute \(a = 3\) into the vertex form: \[ y = 3(x + 1)^2 + 2. \]