Finding quadratic equation

1. Given three points, solve system of three equations using general form:
(1)   y₁ = ax₁² + bx₁ + c
(2)   y₂ = ax₂² + bx₂ + c
(3)   y₃ = ax₃² + bx₃ + c
to find (a, b, c)

2. Given two x-intercepts, p and q, and a point, solve for "a" using intercept form:
y = a(x - p)(x - q)

3. Given vertex, (h, k), and a point, solve for "a" using vertex form:
y = a(x - h)² + k