A parabola with its vertex at (2, 5) and its axis of symmetry parallel to the y-axis can be represented by the equation:
y = a(x - 2)^2 + 5
where a is a coefficient that determines the shape and direction of the parabola.
We can find the value of a by substituting the coordinates of the given point (22, 365) into the equation:
365 = a(22 - 2)^2 + 5
Then, we can solve for a by rearranging the terms and solving for a:
360 = a(20^2)
a = 360 / (20^2)
a = 0.225
Now that we have found the value of a, we can substitute it back into the equation to get the final equation of the parabola:
y = 0.225(x - 2)^2 + 5
To find the value of y when x = 12, we can substitute 12 for x in the equation:
y = 0.225(12 - 2)^2 + 5
y = 0.225(10^2) + 5
y = 2.25 + 5
y = 7.25
Therefore, the value of y when x = 12 is 7.25.