Final answer:
The equation of the parabola passing through (10,12) with vertex (3,11) is y = (1/49)(x - 3)^2 + 11.
Step-by-step explanation:
The parabola that passes through the point (10,12) with the vertex at (3,11) can be represented by the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. To find the value of 'a', we can use the given point (10,12).
We first plug the vertex (3,11) into the equation, giving us y = a(x - 3)^2 + 11. Substituting the coordinates of the point (10,12) into this equation will give us 12 = a(10 - 3)^2 + 11. Simplifying, we get 1 = 49a, which means a = 1/49. Therefore, the equation of the parabola is y = (1/49)(x - 3)^2 + 11.