Every Problem Should Include

Name______Date______Period______

Every problem should include:

Equation in standard form, Vertex, Focus, Directrix, AOS, EOLRs, Graph, direction, p value

PARABOLAS

Standard form for a parabola with vertex (h, k) is (y – k)2 = 4p(x – h) horizontal axis
(x – h)2 = 4p(y – k) vertical axis
Note: p is positive opens toward the positive (up or right)
p is negative opens toward the negative (down or left)
p = the distance from the vertex to the focus and from the vertex to the directrix
2p = distance from focus to parabola
4p = focal width
The vertex is midway between the focus and the directrix.
Always draw the directrix and the axis of symmetry as dashed lines.
Remember y = x2 is
Sketch:
Horizontal axis Vertical axis

Find an equation of the parabola described. Then graph each one.

1. Focus (0, 0); 2. Vertex (0, 0); 3. Vertex (0, 0);

directrix y = 4 focus (0, -6) directrix x = -1

Find an equation of the parabola described. Then graph each one.

4. Focus (0, 2); 5. Focus (3, 4);

directrix x =2 vertex (3,2)

Find the vertex, focus, and directrix of each parabola. Then graph each one.

6. (y – 3)2 = 8(x + 2) 7. (x –2)2 = 4(y – 1)

8. 9. x2 + 16y = 0

Find the vertex, focus, and directrix of each parabola. Then graph each one.

10. x2 = 12y 11. y2 = -8(x + 2)

12. (y – 3)2 = 8(x + 2) 13. (x –2)2 = 4(y – 1)

14. (y + 3)2 = 12(x – 1) 15. (y + 2)2 = -4(x – 3)

16. x2 = -16(y – 2) 17. x2 + 16y = 0

Find an equation of the parabola described. Graph each one.

18. Vertex (0, 0) 19. Vertex (4, 0)

Focus (0, 3) Focus ______

directrix ______directrix y = 6

Equation ______Equation ______

20. Vertex _____ 21. Vertex (2, 3)

Focus (0, 1); Focus (4, 3)

directrix x =2 directrix ______

Equation ______Equation ______

22. Vertex ______23. Vertex (3, -2)

Focus (-1, 0) Focus (3, 1)

directrix y = 4 directrix ______

Equation ______Equation ______