Question

Y = −1 / 4 (x + 4) 2 −1 on a coordinate plane using its vertex, focus, and directrix.

Answer 1

Hello,

Explanation:

do I remind you of the formula :

where (a,b) is the vertex and y=k the directrix

`y=((x-a)^2)/(2(b-k)) +(b+k)/(2) \\\\\\y=-((x+4)^2)/(4) -1 \\\\Using\ identification:\\a=-4\\2(b-k)=-4\\b+k=-2\\\\\left\{\begin{array}{ccc}b-k&=&-2\\b+k&=&-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2b&=&-4\\2k&=&0\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b&=&-2\\k&=&0\\\end{array}\right.\\`

Focus=(-4,-2)

Directrix: y=0

Vertex=(-4,-1)