What is the vertex of # y= (2x-3)^2-x^2-2x+4#?

1 Answer
Dec 29, 2015

#(7/3, -10/3)#

Explanation:

First expand and simplify to get get one term for each power of x.
#y = 4x^2 -12x + 9 - x^2 - 2x + 4#
#y = 3x^2 -14x + 13#
#y = 3(x^2 -(14x)/3 +13/3)#
Use completing the square to put the expression into vertex form
#y = 3(x - 7/3)^2 -49/9 + 13/3) = 3((x-7/3)^2 -10/9)#
#y = 3(x-7/3)^2 -10/3#
Then the vertex occurs where the bracketed term is zero.
Vertex is #(7/3, -10/3)#