What is the vertex form of #y= x(x+3) #?

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Answer 1 · 2015-12-13T19:58:48

#(-3/2,-9/4)#

Distribute the #x#.

#y=x^2+3x#

This is in the #ax^2+bx+c# form of a parabola where

#a=1,b=3,c=0#

The vertex formula of a quadratic equation is

#(-b/(2a),f(-b/(2a)))#

The #x#-coordinate is

#-b/(2a)=-3/(2(1))=-3/2#

The #y#-coordinate is

#f(-3/2)=-3/2(-3/2+3)=-3/2(-3/2+6/2)=-9/4#

Thus, the vertex is #(-3/2,-9/4)#.

graph{x(x+3) [-10, 10, -5, 5]}

Indeed, the vertex is located at the point #(-1.5,-2.25)#.