It's not clear how you determine where the quivers start, i.e., where the 'base' of each one (not the arrow end - the other end) belongs, so here they all start along the line y = 1:
x=0:0.01:1;
y=sqrt(1-x.^2);
c=10;
xq = x(1:c:end); % an arrow at each x
nq = numel(xq);
yq = ones(1,nq); % all starting along the line y = 1
uq = zeros(1,nq); % pointing straight down: u = zero (no x-component)
vq = y(1:c:end)-1; % v = y-1 (from the line y = 1 to the curve y = sqrt(1-x^2))
quiver(xq,yq,uq,vq,'AutoScale','off')
hold on
plot(x,1-x)
plot(x,y)
