What is the vertex of # y= -(2x-1)^2+x^2-6x-2#?

1 Answer
anj
Oct 2, 2017

Simplify, complete the square.
Vertex is #(-1/3, -4/3)#

Explanation:

Expanding:
#y = -(2x - 1)^2 + x^2 - 6x - 2#
#y = -(4x^2 - 4x + 1) + x^2 - 6x - 2#
#y = -4x^2 + 4x - 1 + x^2 - 6x - 2#
#y = -3x^2 - 2x - 3#

Completing the Square:
#y = -3(x^2 + 2/3x) - 3#
#y = -3(x^2 + 2/3x + 1/9 - 1/9) - 3#
#y = -3(x^2 + 2/3x + 1/9) - (-3)(-1/9) - 3#
#y = -3(x + 1/3)^2 - 4/3#

#therefore# Vertex is #(-1/3, -4/3)#

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