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Algebra 2/Trig Midterm review. Solve and graph equations and inequalities Radical equations:

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Presentation on theme: "Algebra 2/Trig Midterm review. Solve and graph equations and inequalities Radical equations:"— Presentation transcript:

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:


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