Quadratic equations packet pdf ESSENTIAL QUESTIONS: Section 8. 4) The graph to the right shows the system of equations comprised of a quadratic function and the linear function !=!, where k is a constant. 6 Quadratic Equations Lesson Objectives: • Student will solve quadratics by using the quadratic formula. Solve: 1. 9 x 1. The General Form of a quadratic equation is: b. 3 To graph quadratic functions in vertex form. 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. Functions: Equations, Tables and Graphs. Explain with complete sentences and diagrams. Solve the equation for t when h = 0 . p. a2_6. 2 – Solving Quadratic Equations Graphically A quadratic equation of the form ax2+bx+c = d can be solved in the following way using your graphing calculator: 1. 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 Solve quadratic equations by inspection (e. Find the maximum height of the acrobat. 2 C. a) It has a max value at y = 5. o Use the discriminant to determine the number of real solutions of a quadratic equation and Solve using the Quadratic Formula - Level 2 1) n2 + 9n + 11 = 0 2) 5p2 − 125 = 0 3) m2 + 5m + 6 = 0 4) 2x2 − 4x − 30 = 0 Solve using the Quadratic Formula - Level 3 5) b2 − 12 b + 10 = −10 6) 6r2 − 5r − 4 = 7 7) 7x2 − 16 = 6 8) 6n2 − 10 n − 16 = 3 Solve using the Quadratic Formula - Level 4 9) 4a2 − 22 = −10 a 10) n2 − May 14, 2020 · 10. Write your answer in radical form. Plug it in a. o Justify each step in solving a quadratic equation by factoring. g. 6 Describe characteristics of quadratic functions and use them to solve real-world problems. Look on the back for hints and answers. Graph the two equations. (WE DID NOT GO THROUGH THIS SECTION YET, BUT PLEASE STILL TRY THESE OUTS. 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. Which quadratic equation could represent this function? A 2 = −4 C = 2−4 B = 2+4 D = 2−4 −7 23. You may need to adjust your window to be sure the intersection(s) is/are visible. 288 Chapter 8 Quadratic Equations, Functions, and Inequalities 32. Use the quadratic formula to find the roots of: 3 2+6 =−2. 5. 8 seconds, is not half of 1. 1 To graph quadratic functions in standard form. −12 x + 7 = 5 − 2 x2 6. 0625 seconds, so Jessie’s lands faster. 6 meters is 5. 4x2 − 9 x + 9 = 0 5. 24. y 25 y 15 y ±20 5 y ±20 5 y ±20 25 y 20 2 25 36. Write an equation for the line of best fit, then. EXAMPLE 2: Solve: 4 2+5 −6=0 SOLUTION We can use the quadratic formula to solve this equation. 5. The highest power of the unknown is 2 Examples 1. 4x2 − 120 = 40 Solve each equation by factoring. 3 IV. 4-5 V. Quadratic Equations zefry@sas. 2 III. Factoring p. Equation must be in one unknown only 2. Quadratic Equations a. ) Steps: 1. Finding the slope. , 2=49), taking square roots, the quadratic formula, and factoring. 2) Which of the following is true about the quadratic function B : T ; L F2 : T equations comprised of a linear equation and a quadratic equation, and which are not possible. *** Example: Steps: – 1. 8t2 + 5. no; Half of 11. 1 seconds. Let Y1= ax2 + bx + c 3. 11) -8 - 5n2 = -8812) 4 - 2a2 = -7 13) 5n2 - 2 = -9214) (m + 8) 2 = 72 9. Go to Y= 2. 1) x2 − 9x + 18 = 0 2) x2 + 5x + 4 = 0 3) n2 − 64 = 0 4) b2 + 5b = 0 1) Which of the following is true about the quadratic function B : T ; : T F4 ; 65. For instance: x2 4 0 is quadratic x2 2x 0 is quadratic x2 2x 1 0 is quadratic x 1 4x2 2x is quadratic b. 1 Quadratic Functions and Equations 1 Reminder on Quadratic Equations Quadratic equations are equations where the unknown appears raised to second power, and, possibly to power 1. Kate recorded the time it took six children of different ages to run one lap around the track. 10. What both methods have in common is that the equation has to be set to = 0. c) It has a max value at y = 4. • Student will apply methods to solve quadratic equations used in real world situations. Solving quadratic equations by factorisation 2 3. 5 To compare properties of two or more functions represented in different ways. 1 II. a. 3x2 − 42 x + 78 = 0 9. This packet covers these topics, which are: I. Solve quadratic equations by inspection (e. Definition: A quadratic equation with one unknown variable is an equation in which there appears an exponent of 2 on the unknown (and sometimes an exponent of 1 as well). 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. Lesson 2 (continued): Graphing Quadratic Equations and Functions Graph each quadratic equation/function on the provided coordinate plane. Writing a linear equation. The equation for the pathway can be modeled by the equation h = - 16t2 + 50t + 4. d) It has a min value at y = 5. Linear Equations A. my CHAPTER 2: QUADRATIC EQUATIONS 1. Solving by Factoring p. Quadratic Models 39. Solving quadratic equations (equations with x2 can be done in different ways. 4_packet. x 2. b) It has a min value at y = 4. Plug a, b and c into the equation above 2. A2. —60 _ q g. 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. After simplifications, equations all reduce to the form ax2 +bx+c=0 and the solutions are (assuming b2 −4ac≥ 0) −b+ √ b2 −4ac 2a and −b− √ b2 −4ac 2a are indeed solutions for the equation 6 2+ −15=0. Write the equation h = −9. Notice that the solutions of the equation ax2 1 bx 1 c 5 0 are the x-intercepts of the Completing the square is another method that is used to solve quadratic equations. 2x2 + 4 x = 70 7. Solving the quadratic equations gives that Jessie’s ball lands in 2. 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 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. O(e Topic 7: Linear vs. , for x2 = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions). Simplify 3. Illustration: 2x2 +x−6 = 0 quadratic in x −16t2 +80t = 0 quadratic in t: The values that satisfy a quadratic (or any polynomial equation) are called roots. x2 + 5 x + 8 = 4 2. 1 Recognize Quadratic Equations and express it in general form General form ax2 bx + c = 0 , where a , b and c are constants , a z 0 Properties 1. We will use two different methods. Solving Quadratic Equations A. 2***Remember the standard form for a quadratic equation is: ax + bx + c = 0. The solution t ≈ 0. 2x 2 + 3x – 1 = 0 is a quadratic equation Create quadratic equations in one variable and use them to solve problems. Let Y2 = d 4. 3(x - 4)2 + 1 = 109 8. 2 B. 10 x2 − 25 = x 2 4. 75 seconds, while Jayla’s lands in 3. You can also use graphing to solve a quadratic equation. ” Steps: 1. Introduction 2 2. Determine the number of solutions Algebra 2 – Practice Solving Quadratic Equations Make sure to practice all the methods we’ve learned. pdf: File Size: 205 kb: File Type: pdf: Download Nov 21, 2014 · Step 1 - Write the equation x 2 + (x + 3) 2 = (x + 6) 2 Step 2 - Solve the equation By using the SQUARE OF A BINOMIAL FORMULA x 2 + x 2 + 6 x + 9 = x 2 + 12 x + 36 2x 2 + 6 x + 9 = x 2 + 12 x + 36 x 2 − 6x − 27 = 0 (x − 9)( x + 3) = 0 x − 9 = 0 x = 9 The shorter leg is 9 x + 3 = 0 x = −3 (This not a valid answer since Any equation that can be expressed in the form ax2 +bx +c =0;a6= 0 is called a quadratic equation. 3x2 = 4 x 3. You have used factoring to solve a quadratic equation. edu. Quadratic Word Problems Short videos: Projectile Word Problem Time and Vertical Height with Graphing Calc Area Word Problem Motion Word Problem The x-intercepts of a quadratic equation are (0,0) and (4,0). Finding Roots of a Quadratic Equation There are 3 primary methods for nding roots to If is negative The equation has solutions with imaginary numbers If is positive The equation has real-number solutions If is a perfect square The equation has solutions that are rational numbers Vertex of a Parabola The X-coordinate of the vertex of the parabola y ax2 bx c is h b a 2. This method is especially helpful when the quadratic equation cannot be solved by simply factoring. Equations of Quadratic Functions from their Graphs Elementary Algebra Skill Solving Quadratic Equations by Factoring Solve each equation by factoring. This equation is in standard form, and =4 =5 =−6 We substitute these values into the quadratic formula and simplify, getting = − ±√ 2−4 2 = Solve Quadratic Equations by Graphing A quadratic equation is an equation that can be written in the standard form ax2 1 bx 1 c 5 0 where aÞ 0. 8 meters. x ±1 4 x ± 1 16 x2 1 16 16x2 1 16x2 1 0 34. 2 To graph quadratic functions in factored form. 8. Directions: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. Solving equations in one variable. Solve each equation with the quadratic formula. Graphing a linear equation. 1) m2 − 5m − 14 = 0 2) b2 − 4b + 4 = 0 3) 2m2 + 2m − 12 = 0 4) 2x2 − 3x − 5 = 0 •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. I. _____ 21) Solve the quadratic equation 5x2 10x 4 using 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. Solving quadratic equations by completing the square 5 4. 12. 4 To transform the graphs of quadratic equations. mkizy suczkw btftpe nmf odmb wpdzuw rojimnk cqfgas mswttg zpzh