Question

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

Answer 1

ANSWER

$(2,-10.75)$

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,

$p = \frac{1}{4}$

The vertex is (2,-11).

The focus is

$(2,-11+ \frac{1}{4} )$

$(2,- \frac{43}{4} )$

$(2,-10.75)$