A hyperextension is an exercise that works the lower back as well as the mid and upper back, specifically the erector spinae

Erector spinae

The Erector spinæ is a muscle group of the back in humans and animals. It is also known as sacrospinalis in older texts. A more modern term is extensor spinae, though this is not in widespread use. The name of the muscle is pronounced e-rec-tor speen-aye, or e-rec-tor spinae-ee.It is really not...

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One method of performing it, called back extension

Back extension

Back extension is a strength training exercise. It is done for strengthening lower back muscles.Using equipment, it can be done by lowering the body from a stand and raising back using the roman chair, or using a back extension machine where body pushes a weight backwards.Without using equipment,...

 involves using a roman chair

Roman chair

The Roman chair is a piece of exercise equipment. The equipment is mainly used for the lower back, but can also target the gluteal muscles and the abdominals. How the equipment is defined, and what the 'Roman chair exercise' is specifically, is an issue that is not clear.-Exercises:Various...

to hold the feet down and hips up.

It can also be performed without equipment, in the bird dog exercise, in a prone position with arms forward. This version involves lifting one arm and the opposing leg at the same time, then releasing.

These strengthen the lower back and are ideal to be used after deadlifts for complete exhaustion of the lower back muscles.