This document is an algebra 2 study guide covering various topics involving graphing and solving quadratic functions and equations. It includes: 1) Graphing quadratic functions in standard and vertex form and writing equations between the forms. 2) Solving quadratic equations by factoring, taking square roots, using the quadratic formula, and completing the square. 3) Working with complex numbers including adding, subtracting, multiplying, dividing and finding absolute values. 4) Graphing and solving quadratic inequalities.

1. Algebra 2
Chapter 5 Study Guide
Graphing with Standard Form
Graph the quadratic function and label the vertex.
1. y = 2x2
– 12x + 19 2. y = – 3x2
+ 5
3. y = ½ x2
+ 4x + 5 4. y = – x2
+ 4x – 2
Graphing with Vertex Form
Graph the quadratic function and label the vertex.
5. y = (x – 1)2
+ 2 6. y = – 2(x + 3)2
– 4
7. y = 3(x + 4)2
+ 5 8. y = – 1/3(x + 1)2
+ 3
Write the equation in standard form. Use FOIL.
9. y = (x + 5)(x + 2) 10. y = – (x + 3)(x – 4)
11. y = 2(x – 1)(x – 6) 12. y = – 3(x – 7)(x + 4)
13. y = (x + 3)2
+ 2 14. y = ½ (8x – 1)2
– 3/2
Solving quadratics by factoring. You have to factor first, before you can solve.
Remember the special factoring patterns like using the box, difference of perfect squares
and binomial theorem.
15. x2
– 12x – 28 = 0 16. 3x2
– 17x = - 10
17. 4x2
– 25 = 0 18. 9x2
+ 16 = - 24x
19. 49x2
– 14x = - 1 20. x2
– 48 = 2x
21. 4x2
– 4x – 3 = 0 22. x2
+ 3x – 18 = 0
23. 2x2
– 17x + 45 = 3x – 5
Solving quadratics by square roots.
24. 2x2
+ 1 = 17 25. 2 – 5x2
= - 9
26. 3(x – 2)2
= 21 27. 4x2
– 6 = 42
28. 1/5(x – 4)2
= 6 29. 1/3(x + 5)2
= 7
Complex numbers.
Be able to give examples of Complex Numbers; be able to fill in a diagram.
Be able to plot complex numbers on a grid.
Be able to add and subtract complex numbers.
Be able to multiply and divide complex numbers. Be able to state conjugate of complex
numbers.
Be able to find absolute values of complex numbers.
p. 277 (17 – 71)
Solving by completing the square.
30. x2
+ 10x – 3 = 0 31. 3x2
– 6x + 12 = 0
32. x2
+ 6x – 8 = 0 33. 5x2
– 10x + 30 = 0
34. x2
+ 4x – 1 = 0 35. 3x2
– 12x + 16 = 0

2. Quadratic Formula.
Be able to use the discriminant to tell how many/what kind of solutions a quadratic has.
Be able to use Quadratic Formula (you don’t have to memorize it).
36. 2x2
+ x = 5 37. 3x2
+ 8x = 35
38. 12x – 5 = 2x2
+ 13 39. -2x2
= -2x + 3
40. -x2
+ 2x = 2 41. x2
= 2x – 5
Quadratic Inequalities.
Be able to shade the region given.
Be able to graph systems of quadratic inequalities (more than one).
Be able to solve quadratic inequalities (using the number line and set notation).
Graph:
42. y < 2x2
– 5x – 3 43. y > -x2
– 2x – 3
44. y < -x2
– 4x + 1 45. y > x2
– 4x + 1
46. y < -x2
+ 9 47. y > x2
+ 4x
y > x2
+ 5x – 6 y < 3x2
Solve:
48. x2
– 6x + 5 < 0 49. 2x2
+ 3x – 3 > 0
50. -x2
– 9x + 36 > 0 51. -3x2
+ x + 7 < 0