Algebra 2/Trig
Worksheet – Parabolas
Parabola A #1 –21 odd
Parabola B #2 – 22 even
Parabola C #23 - 30
Find the vertex, focus and directrix of each parabola, then graph the parabola.
1. (𝑥 − 1) = 8(𝑦 − 2)
2. (𝑦 − 5) = − 6(𝑥 + 3)
3. (𝑦 + 3) = −2𝑥
4. (𝑥 + 1) = 4(𝑦 + 7)
5. (𝑥 − 6) = −4(𝑦 + 3)
6. (𝑦 − 5) = −12(𝑥 + 1)
7. 3(𝑦 − 3) − 𝑥 + 2 = 0
8. (𝑥 + 2) + 𝑦 − 4 = 0
9.
(𝑥 + 5) − 𝑦 = 0
10. 𝑥 − 2(𝑦 − 2) + 3 = 0
Parabolas have a vertex, focus and directrix. In the following problems, two of these are given.
Find the third.
11.
vertex (4, 2); directrix y = - 3
12. directrix y = 2; vertex (2, 4)
13.
vertex (-2, 1); focus (2, 1)
14. focus (- 3, - 1); vertex (1, - 1)
15. focus (1, - 2); directrix y = 12
16. directrix x = - 6; focus (2, 0)
Find the standard form of the equation of the parabola described.
17.
focus (0, 0); directrix x = - 6
18. vertex (4, -4); focus (0, - 4)
19.
focus (3, 4); vertex (3, -1)
20. focus (- 2, 0); directrix y = 3
21.
vertex (0, 0); directrix x = - 1
22. focus (- 2, 1); vertex (- 3, 1)
Find the vertex, focus and directrix of each parabola. Then graph the parabola.
23. 𝑦 = 𝑥
24. 𝑥 + 8𝑦 + 4𝑥 − 4 = 0
25. 4𝑥 = 𝑦 − 4𝑦
26. 𝑦 + 6𝑦 + 2𝑥 + 5 = 0
27. 𝑥 + 10𝑥 + 16𝑦 − 7 = 0
28. 4(𝑥 + 1) = (𝑦 + 3)
29. 𝑥 − 2𝑥 + 2𝑦 + 3 = 0
30. 31 − 4𝑥 − 𝑦 − 2𝑦 = 0