Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

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:

$y=ax^2+bx+c$

The vertex is at:

$V=(h,k)\\h=\frac{-b}{2a}$

The focus falls on the symmetry axis (x=h) of the parabola at:

$F=(h, k+\frac{1}{4a})$

The directrix is a straight line described by:

$y=k-\frac{1}{4a}$

If we are given the parabola:

$y=x^2 + 4x + 4$

Then:

$a=1\\b=4\\h=\frac{-4}{2}\\h=-2\\k=(-2)^2+(-2*4)+4\\k=0\\V=(-2,0)$

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

$F=( -2, 0+\frac{1}{4*1})\\F=(-2, 1/4)$

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

$y=k-\frac{1}{4a}\\y=0-\frac{1}{4a}\\y=-1/(4a)$

The directrix of the parabola is given by the equation y = -1/(4a)