A parabola has vertex $(4,2)$ and passes through $(2,0).$  Enter the equation of the parabola in the form "$y = ax^2 + bx + c$".
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A parabola has vertex $(4,2)$ and passes through $(2,0).$  Enter the equation of the parabola in the form "$y = ax^2 + bx + c$".
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
y = -\frac{1}{2} x^2 + 4x - 6
A parabola has vertex $(4,2)$ and passes through $(2,0).$  Enter the equation of the parabola in the form "$y = ax^2 + bx + c$".
train