What is the vertex of # y = 1/2 (3x + 4)^2 - 5 #?

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Answer 1 · 2016-04-22T13:10:59

#color(blue)("Vertex"->(x,y)->(-4/3,-5)#

Consider the following:

Standard form#->y=ax^2+bx+c#

Vertex form#->y=a(x+b/(2a))^2+k+c#

Where #k=(-1)xxa(b/(2a))^2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("The given equation is not quite in vertex form")#

Write as:#" "y=3/2(x+4/3)^2-5" "# Now it is!

#color(blue)(x_("vertex")=color(brown)((-1)xxb/(2a))color(green)( = (-1)xx4/3 )= -4/3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)(y_("vertex")=color(brown)(k+c) =-5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Vertex"->(x,y)->(-4/3,-5)#

Tony B