7. Solve each equation by using the Quadratic Formula a. 2 x 2 + 4 x − 5 = 0 b. 3x 2 + 7 x + 10 = 0
d. −4 x 2 + 5 x + 8 = 0
e. 2 x 2 − 3 = 7 x
c.
x2 − 9x −1 = 0
f.
4 x 2 + 3x = −6
8. Solve each quadratic equation by using any of the methods you have learned. For each equation, tell which method you used and why you chose that method. 2 a. x 2 + 6 x + 9 = 0 b. 8 x 2 + 5 x − 6 = 0 c. ( x + 4 ) − 36 = 0
Algebra 2a/Trig Homework #8 (9.2) d. x 2 + 2 x = 7
Name__________________________ period_________
9. Reason abstractly. Under what circumstances will the radicand in the Quadratic Formula, x =
−b ± b2 − 4ac , be negative? 2a
If the radicand is negative, what does this tell you about the solutions of the quadratic equation?
10. A player shoots a basketball from a height of 7 ft with an initial vertical velocity of 18 ft/s. The equation −16t 2 + 18t + 7 = 10 can be used to determine the time t in seconds at which the ball will have a height of 10 ft-the same height as the basket. a. Solve by using the quadratic formula.
Algebra 2a/Trig Name__________________________ Homework #8 (9.2) period_________ b. To the nearest tenth of a second, when will the ball have a height of 10 ft?
c. Explain how you can check your answers to part b. P. 150: 21-37 For items 21-28, solve each equation by using the Quadratic Formula. 2 21. x + 12 x + 6 = 0 22. 3x 2 − 5 x + 3 = 0 23. 2 x 2 + 6 x = 25
24. 42 x 2 + 11x − 20 = 0
25. x 2 + 6 x + 8 = 4 x − 3
27. 4 x 2 + x − 12 = 3x 2 − 5 x
28. x 2 − 20 x = 6 x 2 − 2 x + 20
26. 10 x 2 − 5 x = 9 x + 8
Algebra 2a/Trig Name__________________________ Homework #8 (9.2) period_________ Skip 29 & 30 For items 31-36, solve each equation, using any method that you choose. For each equation, tell which method you used and why you chose that method. 2 32. 2 x 2 − 9 x + 5 = 0 33. x 2 + 7 x + 12 = 0 31. ( x + 3) − 25 = 0
34. 3x 2 + x − 14 = 0
35. x 2 + 8 x = 7
36. 4 x 2 − 33 = 0
37. The more concert tickets a customer buys, the less each individual ticket costs. The function c(t ) = −2t 2 + 82t + 5 gives the total cost in dollars of buying t tickets to the concert. Customers may buy no more than 15 tickets. a. Megan spent a total of $301 on concert tickets. Write a quadratic equation that can be used to determine the number of tickets Megan bought.
b. Use the quadratic formula to solve the equation. Then interpret the solutions.
