How do you find the vertex of #y = 3x^2 -6x-4#?

1 Answer
Jul 15, 2015

Convert to vertex form to obtain the vertex at #(1,-7)#

Explanation:

The easiest way to solve this requirement is to rewrite the equation into vertex form:
#color(white)("XXXX")##y = m(x-a)^2+b#
#color(white)("XXXX")##color(white)("XXXX")#which will have a vertex at #(a,b)#

Given #y = 3x^2-6x-4#

Extract #m#
#color(white)("XXXX")##y = 3(x^2-2x) -4#

Complete the square by adding #3(1)# and then subtracting #3# as
#color(white)("XXXX")##y = 3(x^2-2x+1) -4 -3#

Rewrite as a squared binomial and simply
#color(white)("XXXX")##y = 3(x-1)^2 + (-7)#

Since this is in vertex form, we can simply read the vertex off as:
#color(white)("XXXX")##(1,-7)#