Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

1 Answer

Nov 14, 2017

#(2.5,-0.5) min#

Explanation:

#y'=2(x-3)*1+2x-4#
#=> 2x-6+2x-4#
#=> 4x-10#
#=> 2(2x-5)#

#y'=0#
#=>#
#2(2x-5)=0#
#=> 2x-5=0#
#=> 2x=5#
#=> x=5/2=2.5#

#y''=4>0 => min#

#y_((2.5))=(2.5-3)^2+(2.5)^2-4(2.5)+3=#
#=(-0.5)^2+(2.5)^2-10+3#
#=0.25+6.25-7#
#=-0.5#

#(2.5,-0.5) min#

Related questions

See all questions in Quadratic Functions and Their Graphs

Impact of this question

800 views around the world

You can reuse this answer
Creative Commons License