Question

What is the vertex form of `y= x^2+9x-22`?

Answer 1

`y=(x-(-9/2))^2+(-169/4)`

Explanation:

General vertex form:
`color(white)("XXX")y=(x-a)^2+b` with vertex at `(a,b)`

`rarrcolor(white)("XXX")y=x^2+9x-22`

`rarrcolor(white)("XXX")y=x^2+9xcolor(red)(+(9/2)^2)-22color(red)(-(9/2)^2)`

`rarrcolor(white)("XXX")y=(x+9/2)^2-22-81/4`

`rarrcolor(white)("XXX")y=(x-(-9/2))^2+(-169/4)`

which is the vertex form with vertex at `(-9/2,-169/4)`