When you are graphing quadratics‚ it is the same as graphing linear equations but‚ quadratics have the curvy line‚ called a parabola. When you are graphing your points‚ it is best to graph three or more points. You are really going to need to point three or more points‚ because if there are less than three you will not have a correct graph‚ graphing more than three will insure that your graph will be correct. The biggest number that they say you have to graph will most likely not be able to be graphed
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Quadratic functions are used all the time‚ every day‚ all over the world. Even though right now‚ it doesn’t seem like this kind of math is ever going to creep back into our life. That is actually far from true. These math skill are crucial to have if one ever decides to do anything in engineering‚ or something like that. Those types of jobs are now becoming more and more popular‚ because the world is always going to need educated people who know how to construct or refurbish buildings and homes.
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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 profit functions are
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Width (m) Area (m2) 1 11 11 a 10 b 3 c 27 4 d e (2) 3 (b) If the length of the rectangle is x m‚ and the area is A m2‚ express A in terms of x only. (1) (c) What are the length and width of the rectangle if the area is to be a maximum? (3) (Total 6 marks) 5. (a) Solve the equation x2 – 5x + 6 = 0. (b) Find the coordinates of the points where the graph of y = x2 – 5x + 6 intersects the x-axis. Working: Answers: (a) ………………………………………….. (b) .................................
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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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• A quadratic function (f) is a function that has the form as f(x) = ax2 + bx + c where a‚ b and c are real numbers and a not equal to zero (or a ≠ 0). • The graph of the quadratic function is called a parabola. It is a "U" or “n” shaped curve that may open up or down depending on the sign of coefficient a. Any equation that has 2 as the largest exponent of x is a quadratic function. ☺Forms of Quadratic functions: * Quadratic functions can be expressed in 3 forms: 1. General form: f (x) = ax2
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Real World Quadratic Functions MAT222: Intermediate Algebra Argenia L. McCray Professor: Eric Bienstock October 27‚ 2014 Quadratic Functions This week we have been learning the many different quadratic functions. Throughout the world the quadratic functions are being used / or being implicated into their system of employment‚ business‚ and in all schools. To say that the quadratic function has limited/ or less of it many possibilities which is available to be used in solving
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MCR3U0: Unit 2 – Equivalent Expressions and Quadratic Functions Radical Expressions 1) Express as a mixed radical in simplest form. a) c) b) e) d) f) 2) Simplify. a) b) d) e) c) f) 3) Simplify. a) b) c) d) e) f) 4) Simplify. a) d) b) e) f) c) For questions 5 to 9‚ calculate the exact values and express your answers in simplest radical form. 5) Calculate the length of the diagonal of a square with side length 4 cm. 6) A square has an area of 450 cm2. Calculate the side length. 7) Determine
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Introduction The aim of this investigation is to identify the nature of the roots of quadratics and cubic functions. Part One Case One For Case One‚ the discriminant of the quadratic will always be equal to zero. This will result in the parabola cutting the axis once‚ or twice in the same place‚ creating a distinct root or two of the same root. For PROOF 1‚ the equation y=a(x-b)2 is used. PROOF 1 y = 3 (x – 2)2 = y = 3 (x2 – 4x + 4) = y = 3x2 – 12x + 12 ^ = b2 – 4ac = (-12)2 – 4 x 3 x
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