PreCalculus 3.1, 3.2 Review Simplify each expression. !"! !! !"! !!"" 2. 1. ! ! Solve each of the following quadratic equations. Use factoring, square root property, or the quadratic formula. Use each method at least once. Write the exact form of the answer. 3. 𝑥 ! + 9𝑥 + 6 = 0 6. 𝑥 − 4 ! − 2 = −20 4. 𝑥 ! + 12𝑥 + 8 = 0 7. 𝑥 ! − 11𝑥 + 30 = 2 ! 5. 2 𝑥 − 3 + 36 = 0 8. 2𝑥 ! − 11𝑥 + 25 = 𝑥 ! Solve each of the following quadratic inequalities. Show the x-‐intercepts of the related function and sketch a graph. Write the final answer in interval notation. 9. 𝑥 ! + 4𝑥 − 6 > 0 13. 𝑓 𝑥 = 𝑥 ! − 𝑥 − 6; 𝑓(𝑥) > 0 ! 10. – 𝑥 + 1 ≤ 5 14. 𝑓 𝑥 = −𝑥 ! + 1; 𝑓(𝑥) > 0 11. 𝑥 ! − 2𝑥 − 3 ≤ 0 15. 𝑥 ! − 2𝑥 + 2 > 0 ! 12. 𝑥 + 5 ≤ 0 16. The profit made from the sale of Mcfly’s Hoverboards™ can be modeled by the function 𝑃 𝑥 = −0.5𝑥 ! + 175𝑥 − 3300, where x is the number of board made and sold and 𝑃 𝑥 is the profit. What is greatest number of boards that can be made while breaking even? 17. A tennis court is laid out so that the length is 4 more than two times the width. The area is 2400 square feet. Write and solve a quadratic equation to find the dimensions of the court. Round to the nearest tenth. PreCalculus 3.1, 3.2 Review -‐ Answers 1. 8 − 𝑖 2 ! !! ! ! ! 2. + −9 ± 57 2 4. −6 ± 2 7 5. 3 ± 3𝑖 2 6. 4 ± 3𝑖 2 7. 4, 7 3. 8. !!± !" ! 9. 𝑥 ∈ −∞, −2 − 10 ∪ −2 + 10, ∞ 10. 𝑥 ∈ −∞, ∞ 11. 𝑥 ∈ −1, 3 12. 𝑥 ∈ { } 13. 𝑥 ∈ −∞, −2 ∪ 3, ∞ 14. 𝑥 ∈ (−1, 1) 15. 𝑥 ∈ −∞, ∞ 16. 330 17. 33.7 ft by 71.3 ft