The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
(x-h)² = 4a(y-k)
It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).
Therefore
(x -2)² = 4a(y +2)
The parabola passes through the point (3,-1)
(3-2)² = 4*a(-1+2)
1 = 4 a
a = 1/4
The equation of the parabola is
(x-2)² = (y+2)
Therefore The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
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