What value of \(x\) will give the maximum value for \(-x^2- 6x + 12\)?

This is a dome shaped parabola (negative leading x^2 coefficient)

max will be at -b/2a ....do you think you can find that?

-1x^2 - 6x + 12

This is a parbola that turns downward......the x value that maximizes this is just the x coordinate of the vertex =

- b / [2a] = - (-6) / ( 2 * -1) = 6 / -2 = - 3

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