Math 12AP - Quadratics Review

1. Find the sequences of differences (D₁, D₂, D₃, etc) for each of the following sequences to determine what type of sequence they are:

a) {1, 28, 95, 220, 421, 716, …} b) {0, 15, 40, 75, 120, 175, …}

2. Generate the first 6 terms for each sequence:

a) t_n = 2n² – 2n b) t_n = n³ +5n² – 10n – 15 c) t_n = n⁴ – n²

3. Change each equation from general to transformational form by completing the square:

a) b) c)

d) e) f)

g) h) i)

j) k) l)

4. Find the roots of the following equations using whatever method you like.

a) b) c)

d) e) f)

5. Solve the following equations using whatever method you like.

a) b) c)

d) e) f)

g) h) i)

6. Calculate the discriminant for each of the following equations. What does the discriminant tell you about the graph of the function?

a) b) c)

d) e) f)

7. Find the equation of the parabolas that have the following points.

a) Vertex at (0, 0) and another point (4, 8) b) Vertex at (2, -5) and another point (3, 1)

c) Vertex at (-4, 3) and another point (-6, 11) d) Vertex at (-2, 3) and another point (4, 12)