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Parent Function
In mathematics education, a parent function is the core representation of a function type without manipulations such as translation and dilation. For example, for the family of quadratic functions having the general form : y = ax^2 + bx + c\,, the simplest function is : y = x^2, and every quadratic may be converted to that form by translations and dilations, which may be seen by completing the square In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of and . In terms of a new quantity , this expression is a quadratic polynomial with no linear term. By s .... This is therefore the parent function of the family of quadratic equations. For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes. For example, the graph of ''y'' = ''x'' − 4''x'' + 7 ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Completing The Square
In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of and . In terms of a new quantity , this expression is a quadratic polynomial with no linear term. By subsequently isolating and taking the square root, a quadratic problem can be reduced to a linear problem. The name ''completing the square'' comes from a geometrical picture in which represents an unknown length. Then the quantity represents the area of a square of side and the quantity represents the area of a pair of Congruence (geometry), congruent rectangles with sides and . To this square and pair of rectangles one more square is added, of side length . This crucial step ''completes'' a larger square of side length . Completing the square is the oldest method of solving general quadratic equations, used in Old Babylonian Empire, Old Babylonian clay tablets dating from 1800–1600 BCE, and is still taught in elementary algebra c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Curve Sketching
In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features. Basic techniques The following are usually easy to carry out and give important clues as to the shape of a curve: *Determine the ''x'' and ''y'' intercepts of the curve. The ''x'' intercepts are found by setting ''y'' equal to 0 in the equation of the curve and solving for ''x''. Similarly, the ''y'' intercepts are found by setting ''x'' equal to 0 in the equation of the curve and solving for ''y''. *Determine the symmetry of the curve. If the exponent of ''x'' is always even in the equation of the curve then the ''y''-axis is an axis of Reflection symmetry, symmetry for the curve. Similarly, if the exponent of ''y'' is always even in the equation of the curve then the ''x''-axis is an axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Curves
A curve is a geometrical object in mathematics. Curve(s) may also refer to: Arts, entertainment, and media Music * Curve (band), an English alternative rock music group * Curve (album), ''Curve'' (album), a 2012 album by Our Lady Peace * Curve (song), "Curve" (song), a 2017 song by Gucci Mane featuring The Weeknd * ''Curve'', a 2001 album by Doc Walker * "Curve", a song by John Petrucci from ''Suspended Animation (John Petrucci album), Suspended Animation'', 2005 * "Curve", a song by Cam'ron from the album ''Crime Pays (Cam'ron album), Crime Pays'', 2009 Periodicals * Curve (design magazine), ''Curve'' (design magazine), an industrial design magazine * Curve (magazine), ''Curve'' (magazine), a U.S. lesbian magazine Other uses in arts, entertainment, and media * Curve (film), ''Curve'' (film), a 2015 film * BBC Two "Curve" idents, various animations based around a curve motif Brands and enterprises *Curve (payment card), a payment card that aggregates multiple payment cards * Cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Elementary Algebra
Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variable (mathematics), variables (quantities without fixed values). This use of variables entails use of algebraic notation and an understanding of the general rules of the Operation (mathematics), operations introduced in arithmetic: addition, subtraction, multiplication, division, etc. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real number, real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, and builds on their understanding of arithmetic. The use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |