Quadratic equations packet pdf _____ 21) Solve the quadratic equation 5x2 10x 4 using the quadratic formula. Solve each equation with the quadratic formula. 31) f (x) x2 2x 1 Axis of Symmetry: _____ Vertex: _____ Open Up / Open Down: _____ Maximum / Minimum: _____ x y 32) y x2 8x 13 Solving Quadratic Equations Solving quadratic equations (equations with x2 can be done in different ways. y 25 y 15 y ±20 5 y ±20 5 y ±20 25 y 20 2 25 36. Solving quadratic equations by factorisation 2 3. A) 3 5r 19 B) 3 5r 31 C) 6 5r 19 D) 5 5r 5 _____ 22) Which of the following is a solution of the equation 13 36x2 12 when solved by square roots? A) 5 6 B) 6 1 C) 6 5 D) 5 _____ 23) Which is the graph of 1 2 288 Chapter 8 Quadratic Equations, Functions, and Inequalities 32. Solve: 1. 4x2 − 120 = 40 Find k so that the equation 4x2 − kx = −9 has one rational solution. 1) m2 − 5m − 14 = 0 2) b2 − 4b + 4 = 0 3) 2m2 + 2m − 12 = 0 4) 2x2 − 3x − 5 = 0 %PDF-1. 10 x2 − 25 = x 2 4. Introduction 2 2. Step 1: Arrange terms in standard form Step 2: Factor Step 3: Set each factor = 0 Step 4: Solve each mini-equation Ex 6: Solve each equation by factoring. −12 x + 7 = 5 − 2 x2 6. 1) x2 - 8x + 16 = 02) 2n2 - 18n + 40 = 0 3) x2 - 49 = 0 4) 3x2 - 75 = 0 5) 5k2 - 9k + 18 = 4k2 6) x2 - x - 6 = -6 - 7x 7) 3a2 = -11a - 68) 14n2 - 5 = 33n 9) 5k2 + 28 = 27k10) 3n2 - 5n = 8 Solve each equation by taking square roots. Solving Quadratic Equations by Factoring According to the Zero Product Property, if the product of two quantities is equal to zero, then one of the quantities must equal zero. 7 %µµµµ 1 0 obj >/Metadata 1941 0 R/ViewerPreferences 1942 0 R>> endobj 2 0 obj > endobj 3 0 obj >/ExtGState >/ProcSet [/PDF •solve quadratic equations by factorisation •solve quadratic equations by completing the square •solve quadratic equations using a formula •solve quadratic equations by drawing graphs Contents 1. 11) -8 - 5n2 = -8812) 4 - 2a2 = -7 13) 5n2 - 2 = -9214) (m + 8) 2 = 72 Algebra 2 – Practice Solving Quadratic Equations Make sure to practice all the methods we’ve learned. 9. Solve : x2 + x − 6 < 0. Plug it in a. (WE DID NOT GO THROUGH THIS SECTION YET, BUT PLEASE STILL TRY THESE OUTS. 9 x 1. 2x2 + 4 x = 70 7. For instance, if the equation was x2 – 22 = 9x, you would have to subtract 9x from both sides of the equal sign so the equation would be x2 – 9x – 22 = 0. ” Steps: 1. Lesson 2 (continued): Graphing Quadratic Equations and Functions Graph each quadratic equation/function on the provided coordinate plane. Simplify 3. Lesson 2 (continued): Graphing Quadratic Equations and Functions Graph each quadratic equation/function on the provided coordinate plane. For instance, if the equation was x2 – 22 = 9x, you would have to subtract 9x from both sides of the equal sign so the equation Solving quadratic equations (equations with x2 can be done in different ways. 3x2 = 4 x 3. Determine the number of solutions Solve each equation by factoring. ) Steps: 1. 5 Solving Quadratic Equations by the Quadratic Formula (I,E/2) The Quadratic Formula The solutions of the quadratic equation are √ You can read this formula as “x equals the opposite of b, plus or minus the square root of b squared minus 4ac, all over 2a. Look on the back for hints and answers. x2 + 5 x + 8 = 4 2. Sketch the graph of y = −x2 − 2x + 3. 4x2 − 9 x + 9 = 0 5. We will use two different methods. 1 Lesson 2 (continued): Graphing Quadratic Equations and Functions Graph each quadratic equation/function on the provided coordinate plane. 3x2 − 42 x + 78 = 0 9. x ±1 4 x ± 1 16 x2 1 16 16x2 1 16x2 1 0 34. 3(x - 4)2 + 1 = 109 8. Directions: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. Sketch the graph of : . x 2. . Plug a, b and c into the equation above 2. What both methods have in common is that the equation has to be set to = 0. Solving quadratic equations by completing the square 5 4. sus bygw knzxit dcbk dijylcn enxh djjz cvdx xvdb wtfde