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

1 Answer
Alan P.
Dec 7, 2015

#y=(-1)(x-(-1))^2+4#

Explanation:

The vertex form of a quadratic is
#color(white)("XXX")y=m(x-color(red)(a))^2+color(blue)(b)color(white)("XXX")#with vertex at #(color(red)(a),color(blue)(b))#

Given #y=-x^2-2x+3#

Extract the #m# factor from the terms including an #x#
#color(white)("XXX")y= (-1)(x^2+2x) +3#

Complete the square:
#color(white)("XXX")y=(-1)(x^2+2x+1-1) +3#

#color(white)("XXX")y=(-1)(x^2+2x+1) +1 +3#

#color(white)("XXX")y=(-1)(x+1)^2 + 4#

#color(white)("XXX")y=(-1)(x-(color(red)(-1)))^2+color(blue)(4)#
which is the graph{-x^2-2x+3 [-6.737, 5.753, -0.565, 5.675]} vertex form with vertex at #(color(red)(-1),color(blue)(4))#

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