Find the vertex, focus, and directrix of the parabola. Then sketch the parabola. (x + 3) + (y − 2)^2 = 0

Answer 1

The standard form of a parabola is y = a(x-h)² + k when it opens up/down, or x = a(y-k)² + h when it opens right/left. We can see that the "y" term is the one that is being squared, so we can assume that the parabola is going to open right/left. Rearranging the equation to match what we need, we get:

(x + 3) + (y - 2)² = 0

x + 3 = -(y - 2)²

x = -(y - 2)² - 3

From here we can see that a = -1, k = 2 and h = -3. Because the parabola opens right/left, the following must be true:

Axis of symmetry: y = k---->y = 2

Focus: (h + (1/4a),k)---->(-3 + 1/4(-1),2)---->(-3-1/4,2)---->(-13/4,2)

Directrix: x = h - (1/4a)---->x = -3 - (1/4(-1))---->-3 + 1/4---->-11/4

Vertex: (h,k)---->(-3,2)

Because "a" is negative the graph of the parabola opens to the left.

Hope this helps!