Question

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

Answer 1

Answer:

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

the focus of the parabola is:(-2,$\frac{1}{4}$)

the directrix of the parabola is:y=$\frac{-1}{4}$

Step-by-step explanation:

we know that for any general equation of the parabola of the type $y=ax^{2} +b x+c$ the vertex of the parabola is given by (h,k)

where $h=\frac{-b}{2 a}$ and $k=\frac{4 a c-b^{2} }{4a}$

therefore by the given data we have h=-2 and k=0

hence vertex=(-2,0)

the general equation of the parabola of the type $4 a (y-h)=(x-k)^2$ ; the parabola symmetric around the y-axis has the focus from the centre i.e. the vertex (h,k) at a distance a as (h,k+a) and the directrix is given by y=k-a

so focus is $(-2,\frac{1}{4} )$

now the directrix of the parabola is $y=\frac{-1}{4}$.