Question

I just need the answer :)​

Answer 1

• See below

Explanation:

• Equation of (y - k)^2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p

Given is the parabola:

• (y + 1)^2 = (x + 2)

It has a vertex at (-2, -1)

New vertex (-1, -1) requires translation to the right by 1 unit. Which changes the function to:

• (y + 1)^2 = (x + 2 - 1) ⇒ (y + 1)^2 = (x + 1)

For this function the focus and directrix is:

• (y + 1)^2 = (x + 1)
• k = -1, p = 1/4, h = -1

Focus is

• (h +p, k) = (- 0.75, -1)

Directrix is:

• x = -1 - 1/4 = - 1.25