How do I find the quadratic function for a parabola when given the vertex and two points?

Question

1. Vertex: (1,-3) ;; Points: (-1, 4) (3, 4) ;; (OPENS UPWARDS)
2. vertex: (3,-1) ;; Points: (1, 3) (5, 3) ;; (OPENS UPWARDS)
3. vertex: (1, 5) ;; Points: (0, 2) (2, 2) ; (OPENS DOWNWARDS)

Answer 1

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Answer 2

The vertex form of the parabola is A(x-x₀)² + b where x₀ is the abscissa of the vertex.

The 2 parameters can be found from the given points with a system of 2 linear equations which you get from the points.

In the first problem, the 2 given points are symmetric about the axis of symmetry.