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. \(y = \dfrac{-1}{a}(x - h)^2 - k,\ a, h, k \in \mathbb{Z}_{\gt 0}\)