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Algebra 2 Unit 2 REVIEW - Quadratics Name ________________________________ Graph each parabola. Name the vertex and sketch the axis of symmetry (Section 5.1). 1. Standard Form 2. Vertex Form , Axis of Symmetry: y y = (x – 4)2 - 2 y = -x2 + 6x + 1 Vertex ( 3. Intercept Form ) Vertex ( , ) Axis of Symmetry: 1 x 5x 5 5 Vertex ( , ) Axis of Symmetry: Solve each equation by factoring (Section 5.2). 4. 2x2 -16x + 14 = 0 5. 64x2 – 25 = 0 8. Factor using complex numbers x2 + 121 6. x2 – 5x – 24 = 0 7. 16x2 + 56x + 49 = 0 (Section 5.4) Solve each equation using square roots (Section 5.3). 9. 2x2 = 36 10. 4x2 – 8 = 40 11. (x + 8) 2 = 24 Simplify each expression completely and write in standard form (Section 5.4). 12. 169 15. (12 + 15i) – (8 – i) 17. (3 + 12i)(5 – 4i) 13. 81x8 y 7 14. (9 – 4i) + (–12 + 5i) 16. 6(2 – 4i) + 7(1 – 5i) 18. 6i 1 4i 20. Solve: –4(x + 7) 2 = 144 19. Solve: 3x2 - 8 = - 80 Solve by completing the square (Section 5.5). 21. x2 + 8x = 12 22. x2 – 16x + 24 = 0 23. Write in vertex form by completing the square. Then identify the vertex. y = x2 - 12x + 24 (Section 5.5) 24. The impedance in one part of a series circuit is 7 4i ohms, and the impedance in the other part of the circuit is 12 6i ohms. Add these complex numbers to find the total impedance in the circuit (Section 5.4). 25. The area of the rectangle shown is 117 m2. Find the value of x and the dimensions of the Rectangle (Section 5.2). Work: x 2x - 5 x = _______ Dimensions of Rectangle: 26. Niagara Falls in New York is 214 feet high. How long does it take for water to fall from the top to the bottom of Niagara Falls? ( h = –16t2 + h0 ) (Section 5.3). 27. Michael throws a ball upward, and the height h(t) of the ball t seconds later is given by the equation h(t) = -16t2 +45t + 8 (Section 5.6) a) What was the initial velocity of the ball when Michael threw it? b) What is the maximum height reached by the ball and the time at which this height is reached? ____________ at ___________ c) Complete the table to show the heights at the given times: Time (seconds) Height (feet) 0 1 2 d) Find the average rate of change in height from t = 1 to t = 2. Solve using the quadratic formula (Section 5.6). 28. 3x2 – 8x + 5 = 0 29. x2 + 5x – 8 = 0 30. 4x2 + 3x + 2 = 0 31. Describe a quadratic function’s graph that has (Section 5.6): 1. One real solution: 2. Two real solutions: 3. Two imaginary solutions: Graph the following (Section 5.7): 32. f ( x) x 2 4 33. f ( x) x 2 4 x 3 Solve each inequality. Write your answers in interval notation (Section 5.7). 35. x2 – 4x – 45 > 0 34. x2 + x < 56 36. Solve (Section 7.6) x 8 x 4