Question

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

Answer 1

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)`