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The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
That is, h is the x-coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h), and k is the minimum value (or maximum value, if a < 0) of the quadratic function. One way to see this is to note that the graph of the function f(x) = x 2 is a parabola whose vertex is at the origin
[6]: 202–207 If one is given a quadratic equation in the form x 2 + bx + c = 0, the sought factorization has the form (x + q)(x + s), and one has to find two numbers q and s that add up to b and whose product is c (this is sometimes called "Vieta's rule" [7] and is related to Vieta's formulas). As an example, x 2 + 5x + 6 factors as (x + 3)(x ...
Factorization is one of the most important methods for expression manipulation for several reasons. If one can put an equation in a factored form E⋅F = 0, then the problem of solving the equation splits into two independent (and generally easier) problems E = 0 and F = 0. When an expression can be factored, the factors are often much simpler ...
One particular solution is x = 0, y = 0, z = 0. Two other solutions are x = 3, y = 6, z = 1 , and x = 8, y = 9, z = 2 . There is a unique plane in three-dimensional space which passes through the three points with these coordinates , and this plane is the set of all points whose coordinates are solutions of the equation.
From January 2008 to December 2012, if you bought shares in companies when K. Ram Shriram joined the board, and sold them when he left, you would have a 2.1 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
From December 2011 to December 2012, if you bought shares in companies when Edward Malesich joined the board, and sold them when he left, you would have a 0.6 percent return on your investment, compared to a 13.6 percent return from the S&P 500.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: