How do you write the Vertex form equation of the parabola #y=x^2+4x-7#?

1 Answer
Alan P.
Sep 29, 2016

#y=(x-(-2))^2+(-11)#

Explanation:

First recall the general vertex form:
#color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)# with vertex at #(color(red)(a),color(blue)(b))#

Given
#color(white)("XXX")y=x^2+4x-7#

The required value of #color(green)(m)# is clearly #color(green)(1)# and we can ignore it at this point.

We are trying to get a squared binomial: #(x-color(red)(a))^2#

Completing the square in the given equation:
#color(white)("XXX")y=x^2+4xcolor(magenta)(+2^2)-7 color(magenta)(-2^2)#

#color(white)("XXX")y=(x+2)^2-11#

Into proper vertex form:
#color(white)("XXX")y=color(green)(1)(x-color(red)((-2)))^2+color(blue)((-11))#

graph{x^2+4x-7 [-10.84, 9.16, -12.92, -2.92]}

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