What is the vertex form of #y=-3x^2 -2x+5#?

1 Answer
Alan P.
Mar 28, 2017

#color(green)(y=-3(x+1/3)^2+5 1/3)#

Explanation:

Out target is the quadratic vertex form: #y=color(magenta)m(x-color(red)a)^2+color(blue)b#

We are given
#color(white)("XXX")y=-3x^2-2x+5#

Extracting the #color(magenta)m#
#color(white)("XXX")y=color(magenta)(-3)(x^2+2/3x)+5#

Completing the square
#color(white)("XXX")y=color(magenta)(-3)(x^2+2/3xcolor(brown)(+(1/3)^2))+5color(brown)(-(color(magenta)(-3))((1/3)^2))#

#color(white)("XXX")y=color(magenta)(x+1/3)^2+5+1/3#

#color(white)("XXX")y=color(magenta)(-3)(x-color(red)(""(-1/3)))^2+color(blue)(5 1/3)#

This is technically a more correct version than I give in the "Answer" since it clearly identifies the vertex as being at #(color(red)(-1/3),color(blue)(5 1/3))#
but I thought the "Answer" version was easier to read.
(Check with your instructor for the preferred form).

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