Question

A parabola is given by the equation y = x2 + 4x + 4.

Answer 1

Answer with Step-by-step explanation:

A parabola is given by the equation y = x² + 4x + 4.

For a parabola in the form y=ax^2+bx+c

Vertex: (-b/2a, 4ac-b^2/4a)

Focus: (-b/2a, 4ac-b^2+1/4a)

Directrix: y=c-(b^2+1)4a

Here a=1,b=4,c=4

The vertex of the parabola is  : (-2,0)

The focus of the parabola is  : (-2,1/4)

The directrix of the parabola is given by the equation y = -64

Answer 2

Convert the equation into a standard form
y=x2+4x+4
y= (x+2)^2
From the equation
vertex is located at (-2,0)
Solve for a to get the coordinates of the focus, from the equation 
4a=1
a=1/4
Focus is located at (-2, 1/4)
The equation of the directrix
y=-1/4