Question

Olivia is asked to graph a parabola on a coordinate plane. The focus is located at (0,−3) , and the directrix is at 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
0
−1 −74
−4

Answer 1

Find the vertex: midpoint of focus y = -3 and directrix y = 1 is y = (-3+1)/2 = -1, so vertex (0, −1). p = focus_y − vertex_y = −3 − (−1) = −2.

Parabola: x^2 = 4p(y + 1) = −8(y + 1) ⇒ y = −1 − x^2/8.

Now plug in:

- x = 2: y = −1 − 4/8 = −1 − 1/2 = −3/2 (−1.5)
- x = 0: y = −1
- x = −1: y = −1 − 1/8 = −9/8 (−1.125)
- x = −4: y = −1 − 16/8 = −1 − 2 = −3

Completed table:
2 → −3/2 (−1.5), 0 → −1, −1 → −9/8 (−1.125), −4 → −3.