Write the equation of a parabola that opens upwards and has its vertex at the point (2, -3) and passes through the point (4, 1).

To find the equation of the parabola, we start with the vertex form of a parabola, which is given by \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, the vertex is at \((2, -3)\), so we have: \[ y = a(x - 2)^2 - 3. \] Next, we need to find the value of \( a \) by substituting the point \((4, 1)\) into the equation: \[ 1 = a(4 - 2)^2 - 3. \] This simplifies to: \[ 1 = a(2)^2 - 3 \] \[ 1 = 4a - 3 \] \[ 4a = 1 + 3 \] \[ 4a = 4 \] \[ a = 1. \] Now we can write the final equation of the parabola: \[ y = 1(x - 2)^2 - 3 \] or simply, \[ y = (x - 2)^2 - 3. \] Voilà! That's the equation of your parabola! 😊