Find the equation of the parabola with vertex (-2,3) that also passes through (2,1) and is concave downwards

A < 0;

- b / 2a = - 2; = > b = 4a;

-Δ / 4a = 3, where Δ = b^2 - 4ac;

4a + 2b + c = 1 = > c = 1 - 12a;

-Δ / 4a = 3 = > b^2 - 4ac = - 12a = > 16a^2 - 4a + 48a^2 + 12a = 0 = > 64a^2 + 8a = 0 = > a = - 1 / 8, because a < 0;

then, b = - 1 / 2; c = 1 + 3 / 2 = 5 / 2;

y = ( - 1 / 8) x^2 + ( - 1 / 2) x + 5 / 2 = > x^2 + 4x + 8y - 40 = 0.