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Completing the square is the oldest method of solving general quadratic equations, ... = x 2 is a parabola whose vertex is at the origin (0, 0).
The vertex of a parabola is the place where it turns; hence, it is also called the turning point. If the quadratic function is in vertex form, the vertex is ( h , k ) . Using the method of completing the square, one can turn the standard form
The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
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If a < 0, the parabola has a maximum point and opens downward. The extreme point of the parabola, whether minimum or maximum, corresponds to its vertex. The x-coordinate of the vertex will be located at =, and the y-coordinate of the vertex may be found by substituting this x-value into the function.
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This method for completing the square is ancient and was known to the 8th–9th century Indian mathematician Śrīdhara. [12] Compared with the modern standard method for completing the square, this alternate method avoids fractions until the last step and hence does not require a rearrangement after step 3 to obtain a common denominator in the ...