Equation of a parabola with vertical lines of symmetry

Question

What is the equation of a parabola with vertical lines of symmetry where the parabola contains the points (0,2), (1,-3), and (2, 1)

Answer 1

y=a(x-h)^2 + k where (h,k) = vertex and extremum

3 unknowns a,h & k, plug in each point to get 3 equations

(0,2), (1,-3), (2,1)

2 = a(h^2) + k = ah^2 + k

-3 =a(1-h)^2 + k= a^2 -2ah +ah^2 + k

1 =a(2-h)^2 + k = 4a^2 -4ah + ah^2 + k

plot the points, it's an upward opening parabola, with a>0