Question

How do you find the vertex of a parabola `f(x)=x^2+7x+6`?

Answer 1

The vertex is located at `(-7/2,-25/4)`

Explanation:

Given `f(x)=x^2+7x+6`

Complete the square
`color(white)("XXXX")` `=x^2+7x +(7/2)^2 -(7/2)^2 +6`
Simplify into vertex form
`color(white)("XXXX")` `=(x+7/2)^2 -25/4`
or
`color(white)("XXXX")` `=(x- (-7/2))^2+(-25/4)`
`color(white)("XXXX")` `color(white)("XXXX")`which is the vertex form with vertex at `(-7/2,-25/4)`