How do you find the vertex of #y= 3x^2+ 12x10#?
2 Answers
Vertex:
Explanation:
Use completing of the squares to put the equation in standard form:

Factor the
#x# terms:#y = 3(x^2  4x) 10# 
Take
#1/2# of the#x# term coefficient:#1/2 * 4 = 2# :
#(x2)^2# is the completed square. 
Square the value from step 2:
#(2)^2 = 4# 
Multiply the value from step 3 by the factored value
#3# :#4*3 = 12# . This means we need to add#12# to the equation because when we completed the square we subtracted#12# :# 3(x 2)^2 = 3(x^2  4x +4) = 3x^2 +12x 12# 
#y = 3(x 2)^2  10 +12# 
#y = 3(x 2)^2 + 2# 
vertex:
#(2, 2)#
There is a sort of cheat (not really) way of doing this
Vertex
Explanation:
Write as
This part way to completing the square.
Determine y by substitution
Vertex