What is the vertex form of #y= x^2 + 3x - 28 #?

1 Answer
Alan P.
Jan 28, 2016

#y=(x-3/2)^2+(-121/4)#

Explanation:

The vertex form for a parabolic equation is:
#color(white)("XXX")y=m*(x-color(red)(a))^2+color(green)(b)#
with vertex at #(color(red)(a),color(green)(b))#

Given:
#color(white)("XXX")y=x^2+3x-28#

Complete the square:
#color(white)("XXX")y=x^2+3xcolor(blue)(+(3/2)^2) -28 color(blue)(-9/4)#

Rewrite as a squared binomial plus a (simplified) constant
#color(white)("XXX")y=1*(x-color(red)(3/2))^2+(color(green)(-121/4))#
graph{x^2+3x-28 [-41.75, 40.47, -40.33, 0.74]}

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