How do I use the vertex formula to determine the vertex of the graph for #y=2x^2 +11x-6#?

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Answer 1 · 2015-05-03T12:08:21

The vertex form of a quadratic is
#y=m(x-color(red)(a))^2+color(blue)(b)#
when expressed in this form, the vertex is located at
#(x,y)=(a,b)#

For your example:
#y=2x^2+11x-6#

#y=2(x^2+11/2x)-6 " extracting the "m" value"#

#y=2(x^2+11/2x+(11/4)^2 -(11/4)^2)-6# " completing the square"#

#y=2(x+(11/4)) -121/8 -6#

#y=2(x-color(red)((-11/4)))+color(blue)((-169/8)) " simplifying into vertex form"#

The vertex is at
#(x,y) = (-11/4,-169/8)#