* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Algebra II Test Unit Five – Quadratic Functions Good Luck To NON
Survey
Document related concepts
Kerr metric wikipedia , lookup
Equations of motion wikipedia , lookup
Two-body problem in general relativity wikipedia , lookup
Debye–Hückel equation wikipedia , lookup
BKL singularity wikipedia , lookup
Computational electromagnetics wikipedia , lookup
Perturbation theory wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Equation of state wikipedia , lookup
Differential equation wikipedia , lookup
Itô diffusion wikipedia , lookup
Schwarzschild geodesics wikipedia , lookup
Transcript
Algebra II Test Unit Five – Quadratic Functions Good Luck To______________________________________________Period_____Date______________ NON-CALCULATOR SECTION Vocabulary: Define each word and give an example. 1. Parabola 2. Discriminant 3. Imaginary Unit Short Answer: 4. Describe how to find the complex conjugate of a complex number. What is the result of the product of a number and its complex conjugate? 5. Describe how to factor a trinomial of the form a 2ab b . 2 2 Review: 3 4 2 1 6. Find the inverse of the matrix: 7. Write an equation in slope-intercept form for the line parallel to y 3x 6 that passes through the point 8. 1,5 . Find f 4 for f x 1 2 x 6x 3 . 2 Problems: **Be sure to show all work used to obtain your answer. Circle or box in the final answer.** 9. Simplify: a. 3 56 b. 3 8 c. Page 1 of 7 20 10. Graph the quadratic functions. Label the vertex and axis of symmetry on each graph. y 2x2 5 a. b. y x 1 3 2 c. y x2 4x 5 11. Solve the quadratic equations by factoring. a. x 1 0 2 b. 2 x 4 x 30 c. x 8 x 0 2 2 12. Solve the quadratic equations by square roots. a. x 1 8 2 b. 4 x 2 16 c. 4 x 48 2 2 13. Solve the quadratic equation by completing the square: x 4 x 2 0 2 14. Solve the quadratic equation by the quadratic formula: 2 x 3 x 4 2 Page 2 of 7 15. Simplify the following: a. 9 7i 10 6i 16. Write b. 3 2i 4 3i c. y x 2 6 x 8 in vertex form. Find the zeros and the vertex of the function. 17. Solve the quadratic inequalities: a. 25 x 100 0 2 b. 4 x 12 x 0 2 18. Graph the quadratic inequalities: a. y x2 2 x 1 b. y x2 5 Page 3 of 7 3 7i Multiple Choice Questions: Circle the best answer. 19. Solve the equation x 18 x 81 0 by factoring. 2 A. x 9 B. x 9 C. x 9 D. No solution 20. Which is the solution set for 2 x 7 x 1 0 ? 2 A. 7 41 7 41 , 4 4 B. 7 57 7 57 , 4 4 7 57 7 57 , 4 4 7 41 7 41 , D. 4 4 C. 21. Which is the solution set of 6 x 4 77 ? 2 A. 4 77 4 77 , 12 12 B. 4 77 4 77 , 6 6 C. 4 77 4 77 , 12 12 D. 4 77 4 77 , 6 6 22. Use the discriminant to determine the number and types of solutions of the equation 9 x 30 x 25 0 . 2 A. B. C. D. no real solution, 2 imaginary solutions 1 real solution, no imaginary solutions 1 real solution, 1 imaginary solution 2 real solutions Page 4 of 7 23. Which of the following graphs represents the quadratic inequality A. A. B. C. y x2 4x ? D. Page 5 of 7 Algebra II Test Unit Five – Quadratic Functions Good Luck To______________________________________________Period_____Date______________ CALCULATOR SECTION 1. A geyser sends a blast 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 16t 70t . 2 2. a. What is the maximum height of the boiling water? b. How long is the boiling water in the air? From 1990-1993, the number of truck registrations (in millions) in the United States can be approximated by the model R 0.29t 2 45 , where t is the number of years since 1990. During which year were approximately 46.16 million trucks registered? 3. On fourth down, a team is just out of field goal range. The punter is called in to punt. To avoid kicking the ball into the endzone, the punter needs to kick the football high and short. This punt can be modeled by y 0.088x x is the distance (in yards) the football is kicked and y is the height (in yards) the football is kicked. a. Find the maximum height of the football. b. If the punter punted the ball from the 40-yard line, did the ball reach the endzone? Page 6 of 7 2 2.5x 1 , where **Extra Credit: Write a quadratic function in standard form whose graph passes through the given points: 1, 7 , 1, 5 , 2, 1 **Extra Credit: Solve the quadratic equation ax bx c 0 by completing the square. 2 Page 7 of 7