Question

Find the focus and directrix of the parabola y = {(x + 2)2 – 3.

Answer 1

The focus is at (–2,–212) and the directrix is at y = –312.

Explanation:

Find the focus and directrix of the parabola y=12(x+2)2−3.

got the answer right in the test.

Answer 2

• focus: (-2, -2.75)
• directrix: y = -3.25

Explanation:

For focus-to-vertex distance "p", the equation of a parabola with vertex (h, k) can be written as ...

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

Comparing this to your equation, we see that ...

1/(4p) = 1

h = -2

k = -3

Solving for p, we find ...

1/(4p) = 1

1/4 = p . . . . . multiply by p

The parabola opens upward, so this means the focus is 1/4 unit above the vertex, and the directrix is 1/4 unit below the vertex.

• focus: (-2, -2.75)
• directrix: y = -3.25