# Reverse engineering Green Globs

## Line

1. $$y = b,\ b \in \mathbb{Z}_{\gt 0}$$
2. $$y = b,\ b \in \mathbb{Z}_{\lt 0}$$
3. $$y = x$$
4. $$y = -x$$
5. $$y = x + b,\ b \in \mathbb{Z}_{\gt 0}$$
6. $$y = x - b,\ b \in \mathbb{Z}_{\gt 0}$$
7. $$y = -x + b,\ b \in \mathbb{Z}_{\gt 0}$$
8. $$y = -x - b,\ b \in \mathbb{Z}_{\gt 0}$$
9. $$y = mx,\ m \gt 0$$
10. $$y = -mx,\ m \gt 0$$
11. $$y = mx + b,\ m, b \in \mathbb{Z}_{\gt 0}$$
12. $$y = mx - b,\ m, b \in \mathbb{Z}_{\gt 0}$$
13. $$y = -mx + b,\ m, b \in \mathbb{Z}_{\gt 0}$$
14. $$y = -mx - b,\ m, b \in \mathbb{Z}_{\gt 0}$$
15. $$y = mx,\ m \in \mathbb{Q}_{\gt 0}$$
16. $$y = -mx,\ m \in \mathbb{Q}_{\gt 0}$$
17. $$y = mx + b,\ m \in \mathbb{Q}_{\gt 0},\ b \in \mathbb{Z}_{\gt 0}$$
18. $$y = -mx + b,\ m \in \mathbb{Q}_{\gt 0},\ b \in \mathbb{Z}_{\gt 0}$$
19. $$y = mx - b,\ m \in \mathbb{Q}_{\gt 0},\ b \in \mathbb{Z}_{\gt 0}$$
20. $$y = -mx - b,\ m \in \mathbb{Q}_{\gt 0},\ b \in \mathbb{Z}_{\gt 0}$$

## Parabola

1. $$y = x^2$$
2. $$y = -x^2$$
3. $$y = x^2 - k,\ k \in \mathbb{Z}_{\gt 0}$$
4. $$y = -x^2 + k,\ k \in \mathbb{Z}_{\gt 0}$$
5. $$y = (x - h)^2,\ h \in \mathbb{Z}_{\gt 0}$$
6. $$y = -(x - h)^2,\ h \in \mathbb{Z}_{\gt 0}$$
7. $$y = (x + h)^2,\ h \in \mathbb{Z}_{\gt 0}$$
8. $$y = -(x + h)^2,\ h \in \mathbb{Z}_{\gt 0}$$
9. $$y = (x - h)^2 + k,\ h, k \in \mathbb{Z}_{\gt 0}$$
10. $$y = (x - h)^2 - k,\ h, k \in \mathbb{Z}_{\gt 0}$$
11. $$y = (x + h)^2 - k,\ h, k \in \mathbb{Z}_{\gt 0}$$
12. $$y = (x + h)^2 + k,\ h, k \in \mathbb{Z}_{\gt 0}$$
13. $$y = -(x + h)^2 + k,\ h, k \in \mathbb{Z}_{\gt 0}$$
14. $$y = -(x + h)^2 - k,\ h, k \in \mathbb{Z}_{\gt 0}$$
15. $$y = 2x^2 - k,\ k \in \mathbb{Z}_{\gt 0}$$
16. $$y = ax^2 - k,\ a, k \in \mathbb{Z}_{\gt 0}$$
17. $$y = \dfrac{1}{2}x^2 - k, k \in \mathbb{Z}_{\gt 0}$$
18. $$y = \dfrac{1}{10}x^2 - k, k \in \mathbb{Z}_{\gt 0}$$
19. $$y = a(x - h)^2 - k,\ a, h, k \in \mathbb{Z}_{\gt 0}$$
20. $$y = \dfrac{-1}{a}(x - h)^2 - k,\ a, h, k \in \mathbb{Z}_{\gt 0}$$