If the parabola has y = -4 at both x = 2 and x = 3, then since a parabola is symmetric, its axis of symmetry must be between x = 2 and x = 3, or at x = 5/2. Our general equation can then be: y = a(x - 5/2)^2 + k Substitute (1, -2): -2 = a(-3/2)^2 + k -2 = 9a/4 + k Substitute (2, -4): -4 = a(-1/2)^2 + k -4 = a/4 + k Subtracting: 2 = 2a, so a = 1. Substituting back gives k = -17/4. So the equation is y = (x - 5/2)^2 - 17/4 Expanding: y = x^2 - 5x + 25/4 - 17/4 y = x^2 - 5x + 2 (This is the standard form.)
