Question

Medal and fan given for answer!

Determine the vertex, focus, and directrix of the parabola without graphing.

See the equation below:

Answer 1

\[y+(x+2)^2=3\]

Answer 2

Vertex is easy, how much is y when x=-2

Answer 3

3

Answer 4

So what is the vertex?

Answer 5

(-2,3)

Answer 6

Excellent

Answer 7

How do you find the focus now?

Answer 8

Is the parabola concave up or concave down?

Answer 9

Focus is (0,p) or (p,0) so I need to find p. It is concave down.

Answer 10

No not (0,p), it is (-2,p)

Answer 11

Oops, that makes sense since it's translated.

Answer 12

\[
4 \frac 1 4(y-3) =- (x+2)^2
\]
How much is p?

Answer 13

How did you get 4 (1/4) ?

Answer 14

To find p the equation must be
\[
4 p(y-y_0)=(x-x_0)^2
\]
we have 1 in front of (y-3) so
\[
1 = 4 \times \frac 14
\]

Answer 15

How much is p?

Answer 16

1/4

Answer 17

ok, since the parabola is concave down, where is the focus?

Answer 18

(-2,1/4)

Answer 19

No,\[ (-2,3-\frac 14)\]

Answer 20

(-2, 11/4)

Answer 21

The directrix is y= 3+1/4=13/4

Answer 22

The focus must be on the axis of the parabola

Answer 23

Did you understand it?

Answer 24

Yes! Thanks so much.

Answer 25

YW