Question

find the focus, directrix, vertex and axis of symmetry for the parabola
$(y + 2)^{2}=-8(x - 2)$
focus =
directrix =
vertex =
be sure to enter each answer in the appropriate format. hint; what is the appropriate notation for a
line or a point?
graph the parabola. include the directrix and focus with your graph.
clear all draw:

Explanation:

Step1: Identify vertex form parameters

The parabola equation is $(y - k)^2 = 4p(x - h)$, where vertex $(h,k)=(2,-2)$. $4p=-8\Rightarrow p=-2$.

Step2: Calculate focus

Focus: $(h+p,k)=(2-2,-2)=(0,-2)$

Step3: Calculate directrix

Directrix: $x=h-p=2-(-2)=4$

Step4: Determine axis of symmetry

Axis of symmetry: $y=k=-2$ (horizontal parabola, axis is horizontal line through vertex)

Answer:

Focus = (0, -2)
Directrix = x = 4
Vertex = (2, -2)
Axis of symmetry = y = -2

(Note: Graphing instruction requires plotting the vertex (2,-2), focus (0,-2), directrix x=4, and drawing the parabola opening leftward.)