11.1 solve by graphing 2016 ink.notebook. March 22, Page 115 Unit 11 Factoring. Page Solve Quadratics by Graphing and Algebraically

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1 11.1 solve by graphing 2016 ink.notebook Page 115 Unit 11 Factoring Page Solve Quadratics by Graphing and Algebraically Page 117 Page 118 Page 119 1

2 Lesson Objectives Standards Lesson Lesson Objectives Standards Lesson 11.1 Solve Quadratics by Graphing A.APR.3 A.REI.4 F.IF.4 F.IF.7 I will find the zeros of a quadratic function from a graph I will find the solutions of a quadratic equation by finding the zeros on its graph I will identify the zeros of a quadratic graph I will graph a quadratic function using a graphing calculator Press the tabs to view details. Press the tabs to view details. Lesson Objectives Standards Lesson A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. b) Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a) Graph linear and quadratic functions and show intercepts, maxima, and minima. When solving equations algebraically: 1) get the variable squared by itself 2) take the square root of both sides 3) remember BOTH answers + - Press the tabs to view details. 2

3 Solve each equation symbolically. SHOW ALL WORK. 1. x 2 = a 2 = 98 Solve each equation symbolically. SHOW ALL WORK. 5. r = q 2 80 = When looking at a graph, the solutions are the x intercepts. (Where the graph crosses the x axis) y zero or solution zero or solution x x = - 1 x = 4 3

4 Estimate the solutions of each equation using the given graph. (Hint: Where does the graph touch the x axis?) 7. x = x = 0 9. x 2 + 3x 4 = To find the answer using your graphing calculator: 4

5 11.1 solve by graphing 2016 ink.notebook Zoom 6 puts the graph in "standard" 10 by 10 When looking at the T table on your graphing calculator, if you hit +.5 enter, the table wil count by.5's not 1's. Double check your answers! If you are looking at the T table, there should be an x value on the left that makes a y value on the right a "0". That x is one of the solutions. To change it back to count by 1's, you must make sure you are on a WHOLE number FIRST! Then hit + 1 enter, and the table should be counting by 1's again. Use a graphing calculator to solve each equation. If an equation has no solution, say so x2 + x + 6 = x2 7x = x2 + 3x 9 = x2 + x 2 = 0 no solution 5

6 These are different!! Need to get = 0 on one side first Round to the nearest tenth! 14. 3x 2 7x = x 2 + 4x = On Your Whiteboards Solve each equation symbolically. SHOW ALL WORK. 169 = n 2 a) b) 5a 2 = 45 p = = 3m 2 c) d) e) x 2 = 100 6

7 f) x = 0 g) x 2 + 2x + 3 = 0 Use a graphing calculator to solve each equation. If an equation has no solution, say so. h) x 2 3x 10 = 0 x = -2 or 5 i) x 2 3x + = x = -1 or 3 j) x = 1 or 5 x = 2x x = no or solution k) A ball is thrown upward with a velocity of 32 ft / sec. If x is seconds, its height is given by Formula: h = 16x x + 7 Example: x 2-2x = 9 Find when the ball hits the ground by solving: 0 = 16x x + 7 (Look for where it crosses the x axis.) The ball hits the ground at 2.20 seconds. 7

8 On the Worksheet Homework Homework Homework Hint Solve each equation by showing all work. They will have TWO answers each. 1. x 2 = p 2 = = n k 2 =

9 5. r 2 = 2 6. x 2 = 12 Estimate the solutions of each equation using the given graph 9. x 2-5x = x 2 +8x + 16 = 0 7. k = 0 8. n = 0 Estimate the solutions of each equation using the given graph 11. x 2-9 = x 2-2x - 8 = 0 Estimate the solutions of each equation using the given graph x 2 + 2x - 15 = 0 x 2-3x + 2 = 0 9

10 Use the graphing calculator to solve. (Replace 0 with y.) Find the solution. (x intercepts) If there are none, write no solution. Round answers to the nearest tenth. 15. x 2 + 2x 8 = x 2 9x + 18 = x 2 + 7x 4 = x 2 8x + 16 = x 2 3x + 5 = x = x 2 4x = Adrian earned 50 out of 80 points on a test. What percentage did he score on the test? 22. x 2 4x + 9 = x 2 + 2x = 9 10

11 25. Write the equation of the axis of symmetry and find the coordinates of the vertex. Identify the vertex as a maximum or a minimum. Then graph the function. y = 4x 2 8x The sum of two numbers is 18. The difference of the numbers is 4. Write a system of equations that models this situation. DO NOT SOLVE. Variable Used: Equations: Vertex: Axis of sym: Max or Min: Answers: 27. Shawn and Jenny are selling wrapping paper for a school fundraiser. Shawn sold 10 rolls of plain wrapping paper and 6 rolls of shiny wrapping paper for a total of $168. Jenny sold 13 rolls of plain wrapping paper and 6 rolls of shiny wrapping paper for a total of $195. Write a system of equations that models this situation. DO NOT SOLVE. Variable Used: Equations: 1) x = ±9 3) p = ±3 5) r = ±2 7) k = ±12 9) x = 0 or x = 5 11) x = 3 or x = 3 13) x = 5 or x = 3 15) x = 4 or x = 2 17) x = ±3 19) x = 4 21) x = 1.5 or x = ) x = 4.2 or x = ) ( 1, 9), x = 1, max 27) p = # of plain rolls, s = # of shiny rolls 11