Answer:
y = 1/2x^2 - 2x + 1
Explanation:
The equation of the parabola in vertex form is y = 1/2 (x - 2)^2 - 1. By finding the vertex at (2,-1) we plug in the point into the formula y = a(x-h)^2 + k. To convert it to standard form like the equations listed, multiply through the distributive property to clear the parenthesis.
y = 1/2 (x-2)(x-2) - 1
y = 1/2 (x^2 - 4x + 4) - 1
y = 1/2x^2 - 2x + 2 - 1
y = 1/2x^2 - 2x + 1