Enemy movement

[ChaseNYC]

Hi, I'm picking back up on a space shooter I was making a while ago, and I just can't seem to get this one part down... this is actually why i stopped, so hopefully someone can help. I have been working on enemy movement and I have a few different movement types down but I can't seem to get curved movement down. attached is a diagram of what I'm trying to achieve, roughly, I can't even draw a good curved line but I think you get the idea...

the one on the left is easy, just

this._y+=this.speedY+bgSpeed;
this._x+=this.speedX;

with some if statements for when to change the x direction but i can't seem to get a seemless curve down... Any help, hints, ideas would be of great use. I tried the following code which is a complete flop but I'm including it so you know I've tried things and am not just lazily asking for someone to do it for me:

if(this.moveType==3){
			
			if(this._x>=this.startX){
				this.dFrmStart=this._x-this.startX;
			}else if(this.startX>this._x){
				this.dFrmStart=this.startX-this._x;
			}		
			if(this.dFrmStart>this.maxDist){
				this.speedX=this.speedX*(-1);
			}
			
		if(this.dFrmStart==0){
			this.dFrmStart=.01;
		}
			this.speedMod = (this.dFrmStart/this.maxDist);
			this.speedMod = 1 - this.speedMod;
			if(this.speedMod<0.1){
				this.speedMod=0.1;
			}
			if(this.speedMod==0){
				this.speedMod=1;
			}
			
			this._y+=(this.speed)+bgSpeed;
			this._x+=this.speedX*this.speedMod;
				
		}

anyways, thanks in advance...

ChaseNYC