Question

Identify the vertex and directrix of each.
y = x2 + 2x - 4

Answer 1

See below

Explanation:

Convert equation to vertex form
`y=(x-h)^2+k` by completing the square:

`y=x^2+2x-4`

`y+5=x^2+2x-4+5`

`y+5=x^2+2x+1`

`y+5=(x+1)^2`

`y=(x+1)^2-5`

Vertex:

`(h,k)\rightarrow(-1,-5)`

Directrix:

`y=k-(1)/(4a)\rightarrow y=-5-(1)/(4(1))\rightarrow y=-(21)/(4)`