Answer:
Vertex: (-2, 0)
Focus: (-2, 1/4)
Directrix: y = -1/(4a)
Step-by-step explanation:
Given that a parabola has a general form of:
[tex]y=ax^2+bx+c[/tex]
The vertex is at:
[tex]V=(h,k)\\h=\frac{-b}{2a}[/tex]
The focus falls on the symmetry axis (x=h) of the parabola at:
[tex]F=(h, k+\frac{1}{4a})[/tex]
The directrix is a straight line described by:
[tex]y=k-\frac{1}{4a}[/tex]
If we are given the parabola:
[tex]y=x^2 + 4x + 4[/tex]
Then:
[tex]a=1\\b=4\\h=\frac{-4}{2}\\h=-2\\k=(-2)^2+(-2*4)+4\\k=0\\V=(-2,0)\\[/tex]
The vertex of the parabola is (-2, 0)
[tex]F=( -2, 0+\frac{1}{4*1})\\F=(-2, 1/4)[/tex]
The focus of the parabola is (-2, 1/4)
[tex]y=k-\frac{1}{4a}\\y=0-\frac{1}{4a}\\y=-1/(4a)[/tex]
The directrix of the parabola is given by the equation y = -1/(4a)
