Mechanics quick query

When it comes to kinematics, projectiles (at an angle to horizontal) is the motion always symmetrical provided it's acting freely under gravity and starts and stops at the same level?

For example if a ball is projected from the ground and it travels up then back down again, is the time it takes to travel up the same as it does to travel down? In which case if I find the time it takes to reach its maximum height (at v=0) then can I double that time to find the total time of flight?

thanks