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tricky RITZ

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Solving Quadratic Equations A quadratic equation is an equation of the second degree, meaning that for an equation in x, the greatest exponent on x is 2. Quadratics most commonly refer to vertically oriented parabolas—that is, parabolas that open upward or downward. The graph of a vertically oriented parabola has the shape of a rounded "v," and the bottom-most (or top-most) point is called the vertex. The equation for a parabola is usually written in either standard or vertex form; however, the standard form is more commonly used to solve for the x-intercepts, or roots. The standard form is y = ax2+ bx + c for any real numbers a, b, c where a ≠ 0. The vertex form is y - k = a(x - b)2 with vertex (b, k) and where a ≠ 0. Because x-intercepts are the points at which the graph crosses the x-axis, the solutions are always found by substituting 0 for y. The roots are often useful in solving real world problems, and there are three common ways to find the roots: factoring, using the quadratic formula, and completing the square.

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