• 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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Major Problems Involving Children World today is said to have changed drastically due to various causes. It affects each and every people from every level of society‚ including children. Children are affected badly because they are not mature enough to cope with the situation that surrounds them. As the world becomes crueler each day‚ children are looked to be the victim of the situation. Adults seems like they are not playing their roles well in terms of protecting children. Because of that
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"Age" Word Problems (page 1 of 2) In January of the year 2000‚ I was one more than eleven times as old as my son William. In January of 2009‚ I was seven more than three times as old as him. How old was my son in January of 2000? Obviously‚ in "real life" you’d have walked up to my kid and and asked him how old he was‚ and he’d have proudly held up three grubby fingers‚ but that won’t help you on your homework. Here’s how you’d figure out his age for class: First‚ name things and translate the
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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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Mixing Problems 1. All of the mixing problems that we will be dealing with will involve a “tank”.(mixing fluids in a tank) Problem: Consider a tank which initially holds V0 gal of brine that contains a lb of salt. Another brine solution containing b lb of salt/gallon is poured into the tank at rate of gal/min‚ while simultaneously‚ the well-stirred solution leaves the tank at a rate of f gal/min Objective: Find the amount of salt in the tank at any time t 2. The main assumption
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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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Examples of Age word problems : 1. Six years ago Jun was 4 times as old as Joan.In four years‚ he would be twice as old as Joan. How old are they now? 6 years ago joan x jun 4x .. after 4 years joan x+10 Jun 4x+10 4x+10=2(x+10) 4x+10=2x+20 4x-2x=20-10 2x=10 x=5 joan 6 years ago. Now age = 11 Jun 4x‚ = 20‚ 6 years ago. Now age =26 years now 2. At present‚ Pedro’s age is 25percent of his father’s age.Twenty years from now Pedro’s age would be 50percent of his fathers age. How old
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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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QUADRATIC EQUATIONS Quadratic equations Any equation of the form ax2 + bx + c=0‚ where a‚b‚c are real numbers‚ a 0 is a quadratic equation. For example‚ 2x2 -3x+1=0 is quadratic equation in variable x. SOLVING A QUADRATIC EQUATION 1.Factorisation A real number a is said to be a root of the quadratic equation ax2 + bx + c=0‚ if aa2+ba+c=0. If we can factorise ax2 + bx + c=0‚ a 0‚ into a product of linear factors‚ then the roots of the quadratic equation ax2 + bx + c=0 can be found
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compounded quarterly‚ find the present value of P5‚500 for 10years and 9 months. -Deferred Ordinary Annuity *Find the present value of a deferred annuity of P1‚050 a year for 8 years that is deferred 2 years‚ If money is worth 7% effective. -Problem on Amortization *Arlette owes P10‚000 with interest at 12% compounded semi-annually for three years. Find her periodic payment payable semi-annually and construct the amortization table. -Sinking Fund *Paula borrowed P5‚000 from the Baranggay
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