Question

find the focus, directrix, vertex and axis of symmetry for the parabola $(x - 2)^{2}=8(y + 3)$
vertex =
focus =
directrix =
be sure to enter each answer in the appropriate format. hint: what is the appropriate notat line or a point?
graph the parabola. include the directrix and focus with your graph.
clear all draw:
question help:

Explanation:

Step1: Identify vertex form parameters

The parabola equation is $(x - h)^2 = 4p(y - k)$, where vertex is $(h,k)$. Here, $h=2$, $k=-3$, $4p=8$.

Step2: Calculate $p$

$4p=8 \implies p=2$.

Step3: Find vertex

Vertex $(h,k)=(2,-3)$.

Step4: Find focus

Focus is $(h,k+p)=(2,-3+2)=(2,-1)$.

Step5: Find directrix

Directrix is $y=k-p \implies y=-3-2=-5$.

Step6: Find axis of symmetry

Axis of symmetry is $x=h=2$.

Answer:

Vertex = $(2, -3)$
Focus = $(2, -1)$
Directrix = $y = -5$
Axis of symmetry = $x = 2$

(Note: Graphing instructions involve plotting the parabola opening upward with vertex at (2,-3), focus at (2,-1), and directrix line y=-5 on the given grid.)