<p> Algebra II Practice Test Unit Five – Quadratic Functions</p><p>Name______Period_____Date______</p><p>NON-CALCULATOR SECTION</p><p>Vocabulary: Define each word and give an example.</p><p>1. Quadratic Function</p><p>2. Zero (of a function)</p><p>3. Complex Number</p><p>Short Answer:</p><p>4. Describe how to find the absolute value of a complex number. Show graphically how the formula is derived.</p><p>5. What is the discriminant of the quadratic equation ax2 + bx + c = 0 ? Describe what it means if the discriminant is negative, positive, or zero.</p><p>Review: 轾4- 3 6. Find the inverse of the matrix: 犏 臌2- 5</p><p>7. Write an equation in standard form for the line perpendicular to -3x + 2 y = - 5 that passes through the point (2,- 1) .</p><p>2 8. Find f (-2) for f( x) =2 x - 3 x + 1</p><p>Problems: **Be sure to show all work used to obtain your answer. Circle or box in the final answer.** 9. Simplify: 4 108 20 a. b. - c. 225- - 49 9 7</p><p>Page 1 of 7 10. Graph the quadratic functions. Label the vertex and axis of symmetry on each graph. 2 a. y= - x2 +1 b. y=( x -2) + 4 c. y= x2 -2 x - 5</p><p>11. Solve the quadratic equations by factoring.</p><p> a. 4x2 - 25 = 0 b. -9x2 + 12 x - 4 = 0 c. 6 =x2 - x</p><p>12. Solve the quadratic equations by square roots.</p><p>2 a. 5x2 = 100 b. 3( x + 1) + 4 = 22 c. -2x2 = 6</p><p>13. Solve the quadratic equation by completing the square: 2x2 - 4 x + 20 = 0</p><p>14. Solve the quadratic equation by the quadratic formula: 4x2 + 2 x = 5</p><p>Page 2 of 7 15. Simplify the following: 2 3- i a. (-5 - 8i) -( - 4 - 7 i) b. (3+ 2i) c. 2+ 5i</p><p>16. Write y= x2 +8 x - 9 in vertex form. Find the zeros and the vertex of the function.</p><p>17. Solve the quadratic inequalities: a. 9x2 - 16 < 0 b. x2 - 3 x � 10</p><p>18. Graph the quadratic inequalities: a. y< x2 -4 x + 3 b. y� x2 4 x</p><p>Page 3 of 7 Multiple Choice Questions: Circle the best answer.</p><p>2 19. Which graph represents the function y= -4( x + 8 x + 15) ? y y A. 10 B. 10</p><p>5 5</p><p>-10 -5 5 10 x -10 -5 5 10 x</p><p>-5 -5</p><p>-10 -10</p><p> y y 10 10 C. D. </p><p>5 5</p><p>-10 -5 5 10 x -10 -5 5 10 x</p><p>-5 -5</p><p>-10 -10</p><p>20. What are the solutions of the quadratic equation 3x2 + 5 x = - 4 ?</p><p>-5 +i 23 - 5 - i 23 A. x = , 6 6 -5 +i 73 - 5 - i 73 B. x = , 6 6 5+i 23 5 - i 23 C. x = , 6 6 5+i 73 5 - i 73 D. x = , 6 6</p><p>21. Which is one of the appropriate steps in finding the solutions for x2 +8 x - 9 = 0 when solved by completing the square?</p><p>2 A. (x +4) = 25 2 B. (x +4) = 9 2 C. (x +8) = 9 D. (x+9)( x - 1) = 0</p><p>Page 4 of 7 2 - i 22. Write the expression as a complex number in standard form. 3- 2i</p><p>2 1 A. - i 3 2 2 1 B. + i 3 2 8 7 C. - i 13 13 8 1 D. + i 13 13</p><p>2 23. For the scenario below, use the model h= -16 t + v0 t + h 0 , where h = height (in feet), h0 = initial height (in feet), v0 = initial velocity (in feet per second), and t = time (in seconds).</p><p>A cheerleading squad performs a stunt called a “basket toss” where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward, leaving her teammates’ hands 6 feet above the ground with an initial vertical velocity of 15 feet per second.</p><p>When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air?</p><p>1 A. second 16 B. 1 second 9 C. 1 second 16 D. 2 seconds</p><p>Page 5 of 7 Algebra II Practice Test Unit Five – Quadratic Functions</p><p>Name______Period_____Date______</p><p>CALCULATOR SECTION</p><p>1. Old Faithful in Yellowstone Park is probably the world’s most famous geyser. Old Faithful sends a stream of boiling water into the air. During the eruption, the height h (in feet) of the water t seconds after being forced out of the ground could be modeled by h= -16 t2 + 150 t .</p><p> a. What is the initial velocity of the boiling water?</p><p> b. What is the maximum height of the boiling water?</p><p> c. How long is the boiling water in the air?</p><p>2. From 1970 to 1990, the average cost of a new car, C (in dollars), can be approximated by the model C=30.5 t 2 + 4192 , where t is the number of years since 1970. During which year was the average cost of a new car $12,000?</p><p>3. A punter kicked a 41-yard punt. The path of the football can be modeled by y= -0.035 x2 + 1.4 x + 1 , where x is the distance (in yards) the football is kicked and y is the height (in yards) the football is kicked. Find the maximum height of the football.</p><p>Page 6 of 7 4. Solve the quadratic equation ax2 + bx + c = 0 by completing the square.</p><p>Page 7 of 7</p>