Algebra 1B 4.9 Sample Work Show All Work 1 Unit 4 - Quadratic Functions and Equations 4-1 Quadratic Graphs and Their Properties (pg.534) Graph each function. 1. ?(?) = ? XXXXXXXXXX. ?(?) = ?2 − 3...

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Algebra 1B 4.9 Sample Work Show All Work 1 Unit 4 - Quadratic Functions and Equations 4-1 Quadratic Graphs and Their Properties (pg.534) Graph each function. 1. ?(?) = ?2 + 1 2. ?(?) = ?2 − 3 3. ?(?) = −?2 − 2 Domain: Domain: Domain: Range: Range: Range: 4. How is the graph of y = -5?2 + 3 different from the graph of y = -5?2? (Hint: Describe how the graph shifts) 4-2 Quadratic Functions (pg.541) Find the equation of the axis of symmetry and the coordinates of the vertex of each graph of each function: 5. ? = 2?2 + 3 6. ? = −3?2 + 12? + 1 a) Axis of Symmetry: a) Axis of Symmetry: ? = ⬚ ⬚ ⇒ ? = 2( )2 + 3 = b) Vertex: ( ____ , ____ ) b) Vertex: ( ____ , ____ ) Algebra 1B 4.9 Sample Work Show All Work 2 Same as #1 and 2 above but also GRAPH this quadratic function (see Guided Example)… 7. ?(?) = 2?2 + 4? − 1 8. A rock is thrown upward with an initial velocity of 122 feet per second. The height of the rock ,(h), in feet after t seconds is given by the function ℎ(?) = −16?2 + 122? + 10.How long does it take the rock to reach its maximum height? What is the rock’s maximum height. Round to the nearest hundredth, if necessary. 4-3 Solving Quadratic Equations (pg.548) Solve each equation by graphing. If the equation has no real-number solution, write no solution. 9. ?2 − 4 = 0 10. ?2 + 3 = 0 Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. 11. ?2 = 81 12. ?2 − 144 = 0 13. 5?2 − 20 = 0 14. If an object is dropped from a height of 96ft, the function h(t) = -6?2 + 96 gives the height of the object after t seconds. When will the object hit the ground? Algebra 1B 4.9 Sample Work Show All Work 3 15. Fiona is planning to expand her square vegetable garden in her yard. If each side of the original garden is increased by 6 meters, the new total area will be 81 square meters. Find the length of each side of the original garden. 4-4 Factoring to Solve Quadratic Equations (pg.556) Solve each equation 16. (? − 4)(? − 7) = 0 17. ?2 + 3? − 54 = 0 18. 3?2 − 17? + 24 = 0 4-5 Completing the Square (pg.30) Note: This puzzle (fill-in) is a combination of lesson 4 and 5 practice problems. Why did the mathematicians enter a doubles bowling tournament? Directions: Write the letter of each exercise in the box containing the number of the answer. 19. Solve the following Quadratic equation using factoring (lesson 4). Scratch paper is encouraged! O (? − 5)(? + 1) = 0 12 0, -7 R (2? − 8)(2? − 5) = 0 6 8, 3 S ?(? + 7) = 0 4 4, 5 2 A ℎ2 − 5ℎ + 6 = 0 10 -8, -1 E 0 = ?2 + 9? + 8 2 2, 3 B 2?2 − 11? + 12 = 0 7 5, -1 Algebra 1B 4.9 Sample Work Show All Work 4 20. Evaluate the following Quadratic by Completing the Square (lesson 5). A ?2 + 20? + ? 9 -16, 9 R ?2 − 8? + ? 1 -5, 7 I ?2 − 3? + ? 11 16 21. Solve each equation by completing the square. If necessary, round to the nearest hundredth. L ?2 + 7? = 144