UIBezier Path, Node Jump - ios

Question

I'm working on a Mario Clone for Mac and would like to make the player jump on a curved line when the right and up arrow are pressed.I've heard about UIBezierPaths being the solution to this, but sadly I have no clue how to use them.Can someone please explain what code I would write in order to make a UIBezierPath as well as make Mario follow the path in a jump?Thank you.
Somewhat of the way I would like my player to jump:
!http://projects.haskell.org/diagrams/doc/images/d8527a0188182ef5.png
My Player Movements So far:
func jump(){
// 250 , 120
let jumpUp = SKAction.moveTo(y: 250, duration: 0.25)
let jumpDown = SKAction.moveTo(y: 120, duration: 0.25)
let jumpSequence = SKAction.sequence([jumpUp,jumpDown])
player.run(jumpSequence)
}
func userMoveRight(){
player.xScale = 0.23
level.run(SKAction.sequence([SKAction.moveBy(x: -20, y: 0, duration: 0.2)]))
background.run(SKAction.sequence([SKAction.moveBy(x: -20, y: 0, duration: 0.2)]))
question.run(SKAction.sequence([SKAction.moveBy(x: -20, y: 0, duration: 0.2)]))
}
func userMoveLeft(){
player.xScale = -0.23
background.run(SKAction.sequence([SKAction.moveBy(x: 20, y: 0, duration: 0.2)]))
level.run(SKAction.sequence([SKAction.moveBy(x: 20, y: 0, duration: 0.2)]))
question.run(SKAction.sequence([SKAction.moveBy(x: 20, y: 0, duration: 0.2)]))
}
override func keyDown(with theEvent: NSEvent) {
let keyCode = theEvent.keyCode
//Moving Right
if keyCode == 124 {
userMoveRight()
}
//Moving Left
if player.position.x <= 490, background.position.x <= 1513, keyCode == 123 {
userMoveLeft()
}
//Jump
if keyCode == 126 , player.position.y == 120 {
jump()
}
}