1. The parabola opens upward.
2. The vertex is at (0, 0).
3. The axis of symmetry is the y-axis (x = 0).
4. The focus is at (0, 1/4a) if the equation is y = ax²; for y = x², the focus is at (0, 1/4).
5. The directrix is the line y = -1/4a; for y = x², it is y = -1/4.
6. The latus rectum length is 1/a; for y = x², it is 1.
7. The parabola is symmetric about its axis of symmetry.
8. The vertex is the minimum point for an upward-opening parabola.
9. The parabola extends infinitely in the direction it opens.
10. The distance from any point on the parabola to the focus equals its distance to the directrix.
11. The parabola can be shifted horizontally or vertically by changing the equation to y = a(x-h)² + k.
12. The parabola’s width depends on the coefficient 'a'; smaller |a| means wider parabola.
13. The parabola intersects the y-axis at the vertex if no vertical shift is present.
14. The parabola may intersect the x-axis at zero, one, or two points depending on the discriminant.
15. The parabola’s shape remains unchanged under translation; only position changes.
16. The parabola’s orientation (up/down/left/right) depends on the variable squared and the sign of the leading coefficient.
17. The parabola’s focal length is 1/(4a) for y = ax².
18. The parabola’s reflective property: any ray parallel to the axis of symmetry reflects through the focus.
19. The parabola’s equation can be written in standard form, vertex form, or factored form.
20. The parabola’s domain is all real numbers; range depends on orientation and vertex.
Parent Tip: Review the logic above to help your child master the concept of trends in the periodic table worksheet answer key.
