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Name _________________________________________Date _______________ Algebra 2: Mrs. Knox CHAPTER 1–3 Midterm over Spring Break Due Monday April 13th. If not handed in on the 13th there will be 20 points automatically deducted. Complete work in PENCIL! SHOW ALL WORK FOR FULL CREDIT! If necessary show work on separate piece of paper but write all answers on the test. 1. Graph y = 2x2 – 4x + 1. Identify the vertex and axis of symmetry. 2. Factor 25x2 – 121. 3. Solve x2 – 9x – 22 = 0 by factoring. 4. Solve the equation 4x2 – 5x – 6 = 0 by factoring. 5. Solve 5(x – 3)2 = 75 by finding square roots. 6. Write the product as a complex number in standard form. (3 + 2i)(4 – 5i) 7. Write the quotient as a complex number in standard form. 2i 3 4i 8. Solve x2 – 5x + 2 = 0 by completing the square. 9. Use the quadratic formula to solve the equation 3y2 + 7y + 3 = 0. 10. Find the value of the discriminant and give the number and type of solutions of the equation 4x2 – 8x + 3 = 0. 11. Solve x2 – 5x – 24 ≤ 0 algebraically. 12. Evaluate 32–2/5. 2 x 3 13. Evaluate 2 3y 4 14. Simplify (–3x–5y2)–2. 15. Multiply (2x – 1)(3x2 – 5x + 4). 16. Subtract (3x2 + 8x – 2) – (5x2 – x + 6). 17. Factor completely 7x3 – 56. 18. Find all the real zeros of f(x) = x3 – 4x2 – 11x + 30. 19. Find all the zeros of f(x) = x3 – 2x2 + x – 2. 20. Divide (x5 – 3x3 – 2x + 3) ÷ (x + 2) using synthetic division. 21. Use a graphing calulator to graph f(x) = x3 + 5x2 + 2x – 8. Identify the x–intercepts (zeros) 2 22. Simplify 8 3 23. Simplify 4 81x 6 y 8 24. Find f(g(4)) if f(x) = 3x – 5 and g(x) = 7x – 1. 25. Find the following for f(x) = x2 – 2x and g(x) = 4x + 9 a. f(x) + g(x) b.f(g(x)) 26. Write the equation for the inverse of y = 2 x + 1. 3 27. Solve 3x3/4 = 375. 28. Solve x – 5 = 16x . 29. x + 3 = √2𝑥 + 41 30. (From Chapter 1) A rectangular picture frame measures 8 cm by 4 cm. You want to triple the frame’s area by adding the same distance x to the length and the width. Write and solve an equation to find the value of x.What are the new dimensions of the picture frame? 31. (From Chapter 3)You are digging a garden in your backyard. You would like the length to be 5 feet greater than the width. Determine the function A(x) to calculate the area of the garden. What should the dimensions of the garden be if you would like your garden to cover 104 square feet of ground?