Algebra II Final Exam Review Pt 2Ch 4-6

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Algebra II Final Exam Review Pt 2Ch 4-6

Chapter 4

Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and the range of each function. Then Graph the function. **VERTEX FORM**

1.y = (x  2)2 + 32.y =4(x  3)2 + 2

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of each parabola. Then Graph the function. **STANDARD FORM**

3. y =x24x + 14. y =x2 + 2x + 3

Factor and Solveeach expression.

5. x2 + 11x + 28=0 6. x2 + 11x + 24=0

Factor and Solveeach expression.

7. 5x217x + 6=08. 3x2 + 10x + 8=0

Factor and Solve each expression

9. n249=010. 6x2 9=0

Solve each quadratic equation by completing the square.

11. x2 + 10x 1 = 012. x2 + 2x 7 = 0

Solve each equation using the Quadratic Formula.

13. x2 8x + 15 = 014. 3x2 + 5x = 2

Chapter 5

Determine the end behavior of the graph of each polynomial function.

15. y = 3x4 + 6x3x2 + 12 16. y = 50 3x3 + 5x2

Write each polynomial in factored form. Check by multiplication.

17. 2x3 + 10x2 + 12x18. x4x3 6x2

19. 3x3 + 18x227x20. x32x2 + x

Find the real or imaginary solutions of each equation by factoring.

21. x3 + 64 = 022. x3125 = 0

23. x45x2 + 4 = 024. x412x2 + 11 = 0

Divide using long division. Check your answers.

25. (x2 13x – 48) ÷ (x + 3)

Divide using synthetic division.

26. (x38x2 + 17x 10) ÷(x 5)

Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual rational roots. STEPS ON BOARD!!!

27. P(x) = x35x2 + 2x + 828. P(x) = x3 + x217x + 15

29. P(x) = 2x3 + 13x2 + 17x 1230. P(x) = x3x234x 56

31. x4 + 3x321x248x + 80 = 032. x42x3x24x 6 = 0

Chapter 6

Simplify each radical expression.

33. 34.

Multiply and simplify. Assume that all variables are positive.

35. 36.

Divide and simplify. Assume that all variables are positive.

37.

Simplify.

38.

Multiply.

39.

Solve.

40.

Solve. **Will have to FOIL and FACTOR!!!!!

41.

Let f (x) =4x − 1 and g(x) =2x2 +3. Perform each function operation.

42.

Let ƒ(x) = − 3x + 2, , h(x) = − 2x2 +9, and j(x) =5 −x. Find each value or expression.

43.

Find the inverse of each function.

44.