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Determine the equation of a parabola given two points and the axis of symmetry
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The equation of the parabola can be determined using the following steps: 
1. Find the midpoint of the two given points.
2. Use the midpoint to find the axis of symmetry, which should be a vertical line going through the midpoint.
3. From the two given points and the axis of symmetry, calculate the vertex of the parabola.
4. Using the vertex, the axis of symmetry, and one of the given points, calculate the equation of the parabola in the form y = ax^2 + bx + c.