What is the the vertex of #y = (x - 2)^2 + 5x+4 #?

1 Answer
Sep 4, 2016

Vertex#->(x,y)=(-1/2,color(white)(.) 31/4)#

Explanation:

Square the brackets giving:

#y=x^2-4x+4+5x+4#

#y=x^2+x+8#
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Using part of the process of completing the square ( a sort of cheat method, but permitted).

Consider standard form #y=ax^2+bx+c#

Write as #y=a(x^2+b/ax)+c#

In this case #a=1#

In that we have #1x^2# (not normally written this way).

Thus #y=a(x^2+b/ax)+c" "->" "y=(x^2+x)+8#

#color(blue)(x_("vertex")->(-1/2)xx(b/a) " "->" "(-1/2)xx1 = -1/2)#
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Determine #y_("vertex")# by substitution for #x#

#y=x^2+x+8" "->" "color(blue)(y_("vertex")=(-1/2)^2-1/2+8 = 31/4)#

Tony B