What is the vertex form of #y= (5x+2)^2 + 11x(5x+2)+30#?

2 Answers
Shwetank Mauria
Apr 12, 2017

#y=80(x^2+21/80)^2+2279/80#

Explanation:

Let us first simplify this.

#y=(5x+2)^2+11x(5x+2)+30#

#=25x^2+20x+4+55x^2+22x+30#

#=80x^2+42x+34#

#=80(x^2+42/80x)+34#

#=80(x^2+2xx21/80x+(21/80)^2-(21/80)^2)+34#

#=80(x^2+21/80)^2-(21/80)^2xx80+34#

#=80(x^2+21/80)^2-441/80+34#

#=80(x^2+21/80)^2+2279/80#

which is in vertex form and vertex is #(-21/80,2279/80)# or #(-21/80,28 39/80)# and graph appears as follows:

graph{80x^2+42x+34 [-2, 2, -10.9, 149.1]}

Shwetank Mauria
Apr 12, 2017

#y=80(x^2+21/80)^2+2279/80#

Explanation:

Let us first simplify this.

#y=(5x+2)^2+11x(5x+2)+30#

#=25x^2+20x+4+55x^2+22x+30#

#=80x^2+42x+34#

#=80(x^2+42/80x)+34#

#=80(x^2+2xx21/80x+(21/80)^2-(21/80)^2)+34#

#=80(x^2+21/80)^2-(21/80)^2xx80+34#

#=80(x^2+21/80)^2-441/80+34#

#=80(x^2+21/80)^2+2279/80#

which is in vertex form and vertex is #(-21/80,2279/80)# or #(-21/80,28 39/80)# and graph appears as follows:

graph{80x^2+42x+34 [-2, 2, -10.9, 149.1]}

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