Solving Quadratic Equation A quadratic equation can be solved by using: 1. Factorization i) Arrange the unknowns in general form (ax2+bx+c=0) and factorize it 2. Completing the square i) x2-6x+4=0 ii) x2-6x=-4 iii) x2-6x+-622=-4+-622 iv) x2-6x+-32=-4+-32 v) x-32=5 vi) x-3=±5 vii) x=3±5 viii) x=3+5 OR 3-5 ix) x=5.236/0.7369 3. Quadratic formula x=-b±b2-4ac2a * Forming quadratic equation
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contributions that formed the basic element of science. From this basic element came the luxuries we enjoy today. Pythagoras‚ a mathematician‚ proved "the relationship between the legs and the hypotenuse of a right triangle."1 From this‚ he derived the Pythagorean Theorem. This contribution mainly influenced architecture and geometry today. Equally‚ Eratosthenes also influenced architecture and geometry. He developed a method of determining the circumference of the Earth by using geometry. Developed by Archimedes
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above the water respectively. How high is the diving board? 3. A ball is thrown into the air. Its height above the ground‚ h (measured in feet)‚ at any given time after the ball is thrown‚ t (measured in seconds)‚ can be modelled using the quadratic function h(t) = -16t2 + 16t + 32. From what height above the ground was the ball thrown? Solutions: 1. C = 0 Using point (-6‚ 4 ) and (6‚ 4) 4 = a (-6)^2 + (-6)b + c 4 = 36 a -6b + c
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Objective To prove Distance formula = by experimentally Pre-knowledge We know Pythagoras Theorem Area of triangle Some Knowledge about coordinate Rules for signs of Co-ordinates Axes of Co-ordinates Geometrical Representation of quadratic polynomials Material Required Coloured Glazed paper Pair of scissors Geometry box Graph paper Drawing sheet Colour stick Pencil colour Fevistick/ Gum Procedure Let two points P(x1‚y1) and Q(x2‚y2) on graph sheet. And draw a set of perpendicular
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Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry‚ in which‚ given a line L and a point p outside L‚ there exists no line parallel to L passing through p. Elliptic geometry‚ like hyperbolic geometry‚ violates Euclid’s parallel postulate‚ which asserts that there is exactly one line parallel to L passing through p. In elliptic geometry‚ there are no parallel lines at all. Elliptic geometry has other unusual properties. For example‚ the sum of the angles of any
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the first things we learned was that you can make complex equations look simpler by making substitutions. Take the equation: 2tan2-3tan-2=0 To make this look simpler you can substitute u for tan to get: 2u2-3u-2=0 From there you can us the quadratic formula to get: u= -0.5‚ 2 With this you can now say tan=2 and tan=-0.5 which makes solving for much easier. In this case substitutions made solving much easier and less chaotic looking. The next thing we learned was to rewrite equations
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1. Use the Gaussian elimination method to solve each of the following systems of linear equations: (a) −5x1 − 2x2 + 2x3 = 14 3x1 + x2 − x3 = −8 2x1 + 2x2 − x3 = −3 (b) 3x1 − 2x2 + 4x3 = −54 −x1 + x2 − 2x3 = 20 5x1 − 4x2 + 8x3 = −83 2. Find the quadratic equation y = ax2 + bx + c that goes through the points (3‚ 18)‚ (2‚ 9) and (−2‚ 13). 3. Use the Gauss Jordan method to determine the complete solution set for the given system‚ and give one particular nontrivial solution. −2x1 − 3x2 + 2x3 − 13x4
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Objective Linear Bounds y Equality l Inequalities l Problem size m m l l y Nonlinear s Gradient needed y n Solver linpro quapro qld qpsolve optim neldermead optim_ga fminsearch optim_sa lsqrsolve leastsq optim/"nd" optim_moga semidef lmisolve Quadratic y l l s Nonlinear Least Squares Min-Max Multi-Obj. Semi-Def. y y l* n l m s l* l* l l optional y n n For the constraint columns‚ the letter "l" means linear‚ the letter "n" means nonlinear and "l*" means linear constraints
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Comparison of Similar Characters In both the Gus Van Sant directed film Good Will Hunting and J.D. Salinger’s The Catcher in the Rye‚ the antagonists are trying to find the true value of life. While the film is not by any means the visual for the novel‚ the two are often compared most typically because of the antagonists. Both Holden Caulfield and Will Hunting are both capable of exceeding in the world‚ but their cruel living styles act as setbacks to whatever beholds in their respective futures
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|15 | • Display results in a table. Using technology‚ display your results in a discrete graph • Find a quadratic function that shows the relationship between the number of steps and the area Quadratic Formula: y= ax2 + bx+ c [pic] • Plug in the coordinates to the quadratic formula 1) 1= a (1)2 +b (1) – c 2) 3= a(2)2 b(2) +c 3) 6=a(3)2 +b(3) +c 1= a+ b+ c 3=4a+2b+c
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