Question

Olivia is asked to graph a parabola on a coordinate plane. The focus is located at (0,−3)
(
0
,
−
3
)
, and the directrix is at y=1
𝑦
=
1
. Fill in the missing values on the table for the coordinates of the parabola.(1 point)
Complete the Table for the Given Parabola
x-value y-value
2 −4
−
4

0
−1
−
1
−74
−
7
4

−4
−
4

Answer 1

First find the parabola. The vertex is midway between the focus (0, −3) and the directrix y = 1, so the vertex is (0, −1). The distance p from the vertex to the focus is −2, so the equation is

x^2 = 4p(y + 1) = −8(y + 1) --> y = −1 − x^2/8.

Now compute the y-values:

- x = 2: y = −1 − (2^2)/8 = −1 − 4/8 = −3/2 = −1.5
- x = −4: y = −1 − (16)/8 = −1 − 2 = −3
- x = 0: y = −1
- x = −1: y = −1 − 1/8 = −9/8 = −1.125
- x = −7/4: y = −1 − (49/16)/8 = −1 − 49/128 = −177/128 ≈ −1.3828
- x = 4: y = −3

If any of the x-values in your table were different (the image/text looked a little garbled), tell me the exact x-values and I’ll fill in those y-values.