find the maximum of minimum value of a quadratic function

find the maximum of minimum value of a qudartic fucntion, by completing the square
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if the quadratic is  a u shape or what a call a smilie face then it is a minimum if it is a frown or a .. kinda n shape or what i call a frowning face it is maximum normaly the quadratic has  a negitive sign in front of the x^2 to be a frowning face~   ^------^

 also u can tell as in a u you can't go below the lowest point of u and the same with n... u can go above the highest point in n  when the graph is drawn....
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