Fit to just half a parabola

Hi there, I have some simple XY data, and I can fit a quadratic to it as follows:

X = [25.4  30.48  35.56  40.64  45.72  50.8   63.5   76.2];
Y = [12443 9560.9 7381.1 5834.8 4740.6 3926.8 2723.5 2072.4];
p = polyfit(X,Y,2);
x1 = linspace(min(X),max(X),100);
y1 = polyval(p,x1);
figure, plot(X,Y,'o', x1, y1)

What I'd like to do however is to add a constraint and fit only the left half of a parabola. In other words, I would like to constrain my fit such that the underlying model (and therefore result) has a turning point at an X location equal to or greater than my maximum X observation.

How should go about applying such constraints? I'm guessing this is now an optimization toolbox problem rather than just solving a linear set of equations.

Thanks, Sven.