What is the the vertex of #y=(x - 8)^2 + 20x+70 #?

1 Answer
Tony B
Nov 25, 2015

#"the vertex is at: "(x, y)-> (-2,color(white)(.)131)#

Explanation:

Expanding the bracket:
#color(blue)(y=color(brown)((x^2-16x+64 ))+20x+70 #

Collecting like termes

#y=x^2+4x+135.....................................(1)#

Consider the #=4x# term

#color(green)(x_("vertex") = color(black)((-1/2)xx(+4)=)-2)...............(2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Note that the equation must be in the form")#
#color(brown)(y=a(x^2+b/ax) + c ". In your case " a=1 )#

#color(brown)("so you end up with "color(green)( x_("vertex")= (-1/2)xx(b/a)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute (2) into (1) giving:

#y=(-2)^2+4(-2)+135#

#y=4-8+135#

#y=131#

#color(blue)("So the vertex is at: "(x, y)-> (-2,131))#

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