Verified answer

because the horizontal and vertical components of velocity are at right angles

Vx^2 + Vy^2 = V^2 (speed squared) at any point

but Vx is constant and Vy is zero at the top of the arc

so

the minimum speed is Vx (at the top of the arc)

and

Vx = cos(angle) Vi

and angle = 45

Vx = 0.707 Vi

the minimum speed is more than half of Vi

if the angle were 60deg or greater, then there would be a point or points

where speed is half of Vi