1. Algebra 2/Trig Midterm review

2. Solve and graph equations and inequalities Radical equations:

3. Solve and graph equations and inequalities Radical equations:

4. Absolute value Solve and check:

5. Absolute value Solve and check:

6. Quadratic equations Solve:

7. Quadratic equations Solve:

8. #2 Set = o: -43

9. # 3 Factor:

10. quadratics Complete the square to solve: 3x 2 +6x-45=0 When will a ball hit the ground, where will it be after 5 seconds what will it’s max height be? h(t) = -2t 2 +40t+4 t is in seconds

11. Answers: Divide out the 3: 3x 2 +6x-45=0 X 2 +2x -15 =0 X 2 + 2x + 1 = 15 + 1 (x + 1) 2 = 16 X+ 1 = 4 and x + 1 = -4 X = 3 x =-5

12. Graph: When will a ball hit the ground, where will it be after 5 seconds what will is max height be,given h(t) = -2t 2 +40t+4 19.05.94 When t = 20, it hits the ground. After 5 seconds it is 154 ft.high and it reaches a max height of 204 ft.

13. Rational expressions and equations Simplify:

14. Rational expressions Simplify:

15. Solution: Second one:

16. Complex Fractions Simplify:

17. Complex Fractions Simplify:

18. adding Find the lcd and add:

19. adding lcd = (x+1)(x-1)

20. Rational equations Multiply by lcd and solve:

21. Rational equations Lcd = a(a-3) 3 is extraneous

22. grouping Factor and simplify:

23. grouping Factor and simplify:

24. Functions Domain- left to right – x values Range – bottom to top – y values Restricted domains: Set denominators = to 0 Set radicands f -1 (x) inverse: swap x & y and solve Varies inversely: xy = xy

25. Domain and range: Find the largest range for: Y = 3x – 7 For the domain:

26. Domain and range: Find the largest range for: Y = 3x – 7 For the domain: When x = 3, y = 3(3) – 7 =2 Which is the largest value for that domain

27. Examples: Find the domain:

28. Examples: Find the domain: Because it is a denominator and a radical

29. Examples: Find the domain: above x axis: -35

30. Compositions: Second function inside first: Let f(x) = x 2 + 1 g(x) = x - 3

31. Compositions: Second function inside first: Let f(x) = x 2 + 1 g(x) = x - 3

32. Inverses:

33. Multiply each side by the reciprocal

34. Irrationals Simplify:

35. Irrationals Simplify:

36. rationalizing Rationalize using conjugates:

37. rationalizing Rationalize using conjugates:

38. Complex numbers: Remember:

39. Examples: Evaluate:

40. Examples: Evaluate:

41. The discriminant If b 2 – 4ac is…. < 0 (negative) roots are IMAGINARY = 0 roots are rational and equal > 0, perfect square, roots: rational & unequal > 0, not perf. Sq., roots: irrational & unequal Ex: The roots of ax 2 + 12x = -9 are rational and equal when a = ?

42. Answer: ax 2 + 12x = -9 ax 2 + 12x + 9 =0 Set b 2 – 4ac = 0 12 2 – 4(a)(9)=0 144-36a=0 36a=144 a=4

43. Formulas: Quadratics: x= Sum = -b/a Product = c/a

44. Conjugate roots: If 3 – 2i is a root, so is 3 + 2i Find the equation that has the root 4 – i STEPS: 1. Find the sum & the product of 4 – i and its conjugate 2. use x 2 – sum(x) + product = 0

45. SOLUTION: SUM =PRODUCT =

46. circles Write the equation of a circle with center at (-2,3) and a point on the circle (1,1) Graph the circle, find the radius using pythagorean theorem and use equation above.

47. answer Radius = Center = (-2,3)

48. Complete the square for circles Example:

49. Complete the square for circles Example:

50. Solving exponential equations Find like bases and set the exponents equal:

51. Solving exponential equations Find like bases and set the exponents equal: