Answer:
y = (1/8)x^2 - (1/2)x - 1/2.
Step-by-step explanation:
The graph is a parabola.
The distance from any point on the graph to the focus and to the directrix are equal. So:
sqrt ( (x - 2)^2 + (y - 1)^2 ) = y - (-3)
Squaring both sides:
(x - 2)^2 + (y - 1)^2 = (y + 3)^2
x^2 - 4x + 4 + y^2 - 2y + 1 = y^2 + 6y + 9
x^2 - 4x + 5 - 9 = y^2 - y^2 + 2y + 6y
8y = x^2 - 4x - 4
y = (1/8)x^2 - (1/2)x - 1/2 is the required quadratic function.
