Problem 821

Complete the square and find the vertex from of the quadratic function.

f(x) = -x2+6x-38




Factor the coefficient of x2 out of the first two terms.

f(x) = -x2+6x-38


Add 9 to inside and outside the parentheses to complete the square. 9 is added to the outside of the parentheses instead if subtracted the coefficient is -1.


Simplify the square.

=-(x-3)2 – 38 + 9

Simplify the rest of the terms.

f(x) = -(x -3)2 – 29


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