A parabola with vertex (2,0) and axis of symmetry parallel to the y-axis, passes through (3,1) and (-3,t). Find the value of t.

We first need to find the equation of the parabola that has a
vertex (2,0). Now the equation of a parabola with vertex ( h, k) is given
as

y= a(x-h)^2 + k.

=> y = a(x-
2)^2 + 0.

Now the parabola passes through
(3,1)

=> 1 = a( 3 -
2)^2

=> 1 = a

Therefore the
equation of the parabola is y = (x - 2)^2

Now as the point (-3 , t)
lies on the parabola

t = (-3 -
2)^2

=> t = 5^2

=> t =
25

Therefore the required value of t is
25.