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-g or g? and what's -kx?

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http://physics.ucsd.edu/students/cou..._solutions.pdf

Please go to the website and scroll down to question 75a,
why is g=9.8ms^2 is used in the solution instead of g=-9.8ms^2?
Isn't it defined by the question that downward is negative? ( x1=-0.100m )

For part d,
what is -kx in the solution?
Isn't it -1/2kx^2?

Thank you very much!!

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