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WordNet-Online
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Definitions from the WebQuadratic Equation in Standard FormDescription:A quadratic equation in standard form is a polynomial equation of degree 2, where the highest power of the variable is 2. It is expressed in the general form ax² + bx + c = 0, where a, b, and c represent constants, and x represents the variable. Senses:Sense 1: Mathematical DefinitionIn mathematics, a quadratic equation in standard form is a second-degree equation with three coefficients that represents a parabolic curve. Sense 2: Algebraic RepresentationIn algebra, the standard form of a quadratic equation is characterized by the presence of the squared term as the leading coefficient. Usage:Example 1: Solving a Quadratic EquationTo find the solutions of a quadratic equation in standard form, one can use various methods such as factoring, completing the square, or applying the quadratic formula. For instance, consider the equation 3x² + 2x - 5 = 0. By solving this quadratic equation, we can determine the values of x that satisfy the equation. Example 2: Graphing a Quadratic EquationBy plotting the graph of a quadratic equation in standard form, one can visualize the shape of the parabola and determine its key features, such as the vertex, axis of symmetry, and intercepts. An example is y = 2x² - 4x + 1, where analyzing the graph provides insights into the behavior of the function. Possible Related Products: | ||||
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