What is the vertex of # y=-3x^2-4x+2 #?

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Answer 1 · 2015-12-04T03:23:00

#(-2/3,10/3)#

The vertex of a quadratic equation can be found through the vertex formula:

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

The letters represent the coefficients in the standard form of a quadratic equation #ax^2+bx+c#.

Here:
#a=-3#
#b=-4#

Find the #x#-coordinate of the vertex.

#-b/(2a)=-(-4)/(2(-3))=-2/3#

The #y#-coordinate is found by plugging #-2/3# into the original equation.

#-3(-2/3)^2-4(-2/3)+2=-3(4/9)+8/3+2#
#=-4/3+8/3+6/3=10/3#

Thus, the vertex is located at the point #(-2/3,10/3)#.

This can also be found through putting the quadratic into vertex form #y=a(x-h)^2+k# by completing the square.

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

#y=-3(x^2+4/3x+color(blue)(4/9))+2+color(blue)(4/3)#

#y=-3(x+2/3)^2+10/3#

Again, the vertex is located at the point #(-2/3,10/3)#.