Turn it around

First figure gives spring force $F_{x}$ versus position x for the spring-block arrangement of second figure. The scale is set by $F_{s} = 160N$ . This relation holds up to x =± 20 cm. We release the block at x = 12 cm. The mass of the block is 2 kg and the friction between the block and the floor is negligible.

Q : If the block is moving at $v_{x} = +\sqrt{24}$ m/s at x = 2 cm, what are the locations of turning points?