NAME: __________________________________________ DATE: __________________ REVIEW FOR QUADRATICS TEST 1 ALG II CP1 I. Graphing from Vertex Form – Graph the following functions (a) (b) II. Graphing from Factored Form (a) (b) III. Graphing from Standard Form by Completing The Square – Graph the following functions by completing the square to get vertex form (a) (b) IV. Graphing from Standard Form using –b/2a – Graph the following
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LESSON 3 - 6 : The Zeros of a Quadratic Function MCR3U1 (Nature of the Roots) MINDS ON... The demand to create automotive parts is increasing. BMW developed three different methods to develop these parts. The profit function for each method is given below‚ where y is the profit and x is the quantity of parts sold in thousands: PROCESS A: P(x) = -0.5x2 + 3.2x –5.12 PROCESS B: P(x) = -0.5x2 + 4x – 5.12 PROCESS C: P(x) = -0.5x2 + 2.5x – 3.8 The graphs of the corresponding
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Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
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Tak Nga Secondary School 2010-2011 Mid-year Exam Form 4 Mathematics (Paper I) Time allowed: 1 hour 15 minutes Class：________ Name：__________________( ) Marks: ________/ 60 Instructions: 1. Write your name‚ class and class number in the spaces provided on this cover. 2. This paper consists of THREE sections‚ A(1)‚ A(2) and B. Each section carries 20 marks. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided. Supplementary answer sheets will be supplied on request.
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1. The perimeter of this rectangular field is 220 m. One side is x m as shown. Wm xm (a) Express the width (W) in terms of x. (b) Write an expression‚ in terms of x only‚ for the area of the field. (c) If the length (x) is 70 m‚ find the area. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (c) ………………………………………….. (Total 4 marks) 1 2. The diagram shows the graph of y = x2 – 2x – 8. The graph crosses the x-axis at the point A‚ and has a vertex at B. y A x O B (a)
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Real World Quadratic Functions Maximum profit. A chain store manager has been told by the main office that daily profit‚ P‚ is related to the number of clerks working that day‚ x‚ according to the function P = −25x2 + 300x. What number of clerks will maximize the profit‚ and what is the maximum possible profit? In order to find the point at which profit is maximized‚ I must find the critical points of the first derivative of the equation. Coefficient of x^2 is negative‚ so
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QUADRATIC FUNCTIONS (WORD PROBLEMS) 1. The area of a rectangle is 560 square inches. The length is 3 more than twice the width. Find the length and the width. Representation: Let L be the length and let W be the width. The length is 3 more than twice the width‚ so The area is 560‚ so Equation: Plug in and solve for W: Solution: Use the Quadratic Formula: Since the width can’t be negative‚ I get . The length is 2. The hypotenuse of a right triangle is 4 times the smallest side. The third
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Real World Quadratic Functions Read the following instructions in order to complete this assignment: 1. Solve problem 56 on pages 666-667 of Elementary and Intermediate Algebra. 2. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay‚ please make sure to include: o An explanation of the basic shape and location of the graph and what
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Earliest Methods used to solve Quadratic Equation 1. Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia‚ from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.[7] In respect of time they fall in two distinct groups: one from the Old Babylonian period (1830-1531 BC)‚ the other mainly Seleucid from the last three or four centuries BC
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Quadratic equation In elementary algebra‚ a quadratic equation (from the Latin quadratus for "square") is any equation having the form where x represents an unknown‚ and a‚ b‚ and c represent known numbers such that a is not equal to 0. If a = 0‚ then the equation is linear‚ not quadratic. The numbers a‚ b‚ and c are the coefficients of the equation‚ and may be distinguished by calling them‚ the quadratic coefficient‚ the linear coefficient and the constant or free
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