Since the Lagrange Points are a sweet spot in space to orbit an object, why hasn't NASA investigated?

Question

Why hasn't NASA investigated the Lagrange points which are the mathematically predicted points in the orbit of the earth or any planet where an object can with no power remain in orbit forever.  I do not understand the math or the details, but from what I have read it is a spot where the gravity of the earth, moon and sun are all perfectly balanced and equal to zero effect upon any object within the area.  I know that recently in the news there was an NEO discovered in one of the predicted Lagrange points.  Does anyone know about any future explorations planned to discover the potential of these points for future space habitations and missions to other planets and space exploration in general.

? · Accepted Answer

There are several satellites located at the Lagrange points, notably SOHO and the STEREO satellites.

grayure · Answer

The Stanford Torus project suggested locating space colonies at the L5 point.  There are also suggestions that space probes should move around the solar system using such points of equilibrium, of which, considering the large number of massive objects orbiting the Sun, there are many.

Alan · Answer

Many objects have been discovered at the Jovian points and now one at the earth point.

Silent · Answer

What makes you think they haven't?

The link below has a list of seven spacecraft operating at Sun/Earth Lagrangian points, and one operating at an Earth/Moon Lagrangian point. It also lists four more that are planned for the future.

Anonymous · Answer

They have.

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Since the Lagrange Points are a sweet spot in space to orbit an object, why hasn't NASA investigated?

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