1. No category

Algebra II Honors WKST
10-5 Conic Sections: Parabolas
Name: _____________________________
Date: _________________ Period: ______
1. What is the equation of a horizontal parabola? __________________________________________________________
2. What is the equation of a vertical parabola? ____________________________________________________________
3. What is the equation of a horizontal directrix? ___________________ 4. Vertical directrix? ___________________
For each parabola, graph the function and label the directrix and focus point. Then, determine how it opens
(horizontal/vertical), vertex, focus point, directrix, and axis of symmetry.
5. y =
1 2
x
12
1 2
y
4
6. x =
7. ( y − 3) 2 = −8 ( x + 1)
Circle one: Horizontal/Vertical
Circle one: Horizontal/Vertical
Circle one: Horizontal/Vertical
Vertex: ______ Focus: _______
Vertex: ______ Focus: _______
Vertex: ______ Focus: _______
Directrix: _______ AOS: _______
Directrix: _______ AOS: _______
Directrix: _______ AOS: _______
8. ( x − 2) 2 = −12 y
10. y −
9. 24( x + 4) = ( y − 3) 2
1
= x2
2
Circle one: Horizontal/Vertical
Circle one: Horizontal/Vertical
Circle one: Horizontal/Vertical
Vertex: ______ Focus: _______
Vertex: ______ Focus: _______
Vertex: ______ Focus: _______
Directrix: _______ AOS: _______
Directrix: _______ AOS: _______
Directrix: _______ AOS: _______
Find the focus and the directrix of the parabola. The vertex of the parabola is (0, 0).
11. −12 x =
F: ______
1 2
y
2
D: ______
12. x = −
1 2
y
20
F: ______
13.
D: ______
1 2
x =y
16
F: ______
D: ______
Use the given characteristics to answer the following questions.
14. A parabola has the vertex of (0, 0) and a focus of (-3, 0). Determine the equation and the directrix.
15. A parabola has a focus point of (4, 6) and a directrix of x=0.
16. The equation given is − x = ( y − 2) 2 . Determine the vertex, focus, and directrix.
17. The equation given is 4( y + 3) = ( x − 1) 2 . Determine the vertex, focus, and directrix.
18. A focus point of (–2, 1) and vertex is (–3, 1). Determine the equation and the directrix.
⎛3
⎝2
⎞
⎠
19. The vertex of ⎜ , 0 ⎟ and the directrix is x = 0. Find the equation and focus point.
20. A vertical parabolic communications antenna has a focus 6 ft from the vertex of the antenna. Determine the equation.
Match the graph with the appropriate equation
21. ( y + 4) 2 = 4( x − 1)
22. ( y − 1) 2 = −16( x + 3)
23. ( y − 1) 2 = −12( x − 2)
24. ( y − 3) 2 = 4( x + 1)
25. ( x + 2) 2 = −16( y + 1)
26. ( x − 2) 2 = −12( y + 1)
A.
B.
C.
D.
E.
F.