Question

What is the vertex form of `y=x^2+7x-3`?

Answer 1

`y= (x+7/2)^2 - 61/4` or `4y = (2x+7)^2 -61`

Explanation:

For a quadratic of the form `y=ax^2 +bx +c` the vertex form is `y = a[(x+b/(2a))^2 -(b/(2a))^2] +c`
In this case that gives us
`y = (x+7/2)^2 - 49/4 - 3`
`y= (x+7/2)^2 - 61/4`

The vertex is then `(-7/2, -61/4)`

Multiplying throughout by `4` gives
`4y = (2x+7)^2 -61`