Chandler Unified School District



Name______________________________________________________________________Date:___________________________ Hour: ____The following are some problems to help you study for your Unit 2 Test. In addition to problems like these, you should review problems from your notes, homework assignments, and quiz to help you prepare. Lesson 3.1Solve each quadratic equation by taking square roots. Tell whether each solution is real or imaginary. Give exact answers. Express imperfect roots in simplified radical form.1. 2x2-16=02. -5x2+9=03. 4x2=x2-424. x2+12=05. 4x2+11=6Solve each quadratic equation by factoring. (Zero Product Property: The product of two numbers is 0 if and only if at least one of the numbers is zero)6. x2+7x+12=07. -2x2+7=-18. x2-60=4For 9-10, use the model h(t) = h0 - 16t2. Round answers to the nearest tenth.9. A bridge is 38 feet above a river. How many seconds does it take a rock dropped from the bridge to pass by a tree limb that is 10 feet above the water?10. A seagull drops a fish 15 feet above the surface of a pond. How long will it take for the fish to hit the water?Lesson 3.2Add or Subtract the complex numbers. To add and subtract complex numbers, add or subtract the real parts and the imaginary parts separately11. -7+2i+(5-11i)12. 18+27i-(2+3i)Multiply the complex numbers. To multiply complex numbers, we use the FOIL(distributive property) method to distribute. Remember: i2=-113. (4+9i)(6-2i)14. (-3+12i)(7+4i)Lesson 3.3Solve each equation by completing the square. State whether the solutions are real or non-real.15. x2-2x+7=0 16. 2x2+3x+4=017. A ball is thrown in the air with an initial vertical velocity of 14 m/s from an initial height of 2 m. The ball’s height h (in meters) at time t (in seconds) can be modeled by the quadratic function ht=-4.9t2+14t+2. Does the ball reach a height of 12 m? Write an equation and use the discriminant to answer.Solve each equation using the quadratic formula. x=-b±b2-4ac2a18. -5x2-2x-8=019. 7x2+2x+3=-1Lesson 4.1Write the equation of each circle.20. The circle with center C(-3, 2) and radius r = 4.21. The circle with center C(-4, -3) and containing the point P(2, 5).Graph each circle after writing the equation in Standard Form. Identify its center and radius.22. 4x2+4y2+8x-16y+11=023. x2+y2+4x+6y+4=0370522519939000020066000Lesson 4.21295409525Vertical ParabolaHorizontal Parabolax-h2=4p(y-k) or 14px-h2=(y-k) y-k2=4p(x-h) or 14py-k2=(x-h)Tool Box0Vertical ParabolaHorizontal Parabolax-h2=4p(y-k) or 14px-h2=(y-k) y-k2=4p(x-h) or 14py-k2=(x-h)Tool BoxFind the equation of the parabola from the description of the focus and directrix. Then make a sketch showing the parabola, the focus, and the directrix.24. Focus (-8, 0), directrix x = 8 25. Focus (3, 2), directrix y = 0.36099753111500left825500Convert the equation to the standard form of a parabola. Then plot the focus, directrix, and graph the parabola with the vertex and at least two other specific points.26. x2-4x-4y+12=027. y2+2x+8y+18=0-10477512382500364807514478000Lesson 4.3Solve each linear-quadratic systems algebraically.28. y=14x-323x-2y=1329. x-6=-16y22x+y=6right698500Solve the given linear-quadratic system graphically.30. y+3x=0y-6=-3x231. The owners of a circus are planning a new act. They want to have a trapeze artist catch another acrobat in mid-air as the second performer comes into the main tent on a zip-line. If the path of the trapeze can be modeled by the parabola y=14x2+16 and the path of the zip-line can be modeled by y=2x+12, at what point can the trapeze artist grab the second acrobat?Lesson 4.415430523304500Solve the system algebraically. Feel free to check your answers with matrices32. 33. 154305381000 ................
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