Question

Find the focus for y=x^2+4x-7

Answer 1

`(2,-10.75)`

Step-by-step explanation

The given function is

`y = {x}^(2) - 4x - 7`

We rewrite this function to obtain,

`(y + 11) = {( x- 2)}^(2)`

We now compare this function to

`(y - k) = 4p {( x- h)}^(2)`

We have

`4p = 1`

This implies that,

`p = (1)/(4)`

The vertex is (2,-11).

The focus is

`(2,-11+ (1)/(4) )`

`(2,- (43)/(4) )`

`(2,-10.75)`