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In 2D and shooting on a horizontal plane, parabola of safety can be represented by the equation y = u 2 2 g − g x 2 2 u 2 {\displaystyle y={\frac {u^{2}}{2g}}-{\frac {gx^{2}}{2u^{2}}}} where u {\displaystyle u} is the initial speed of projectile and g {\displaystyle g} is the gravitational field.
For the parabola, the standard form has the focus on the x-axis at the point (a, 0) and the directrix the line with equation x = −a. In standard form the parabola will always pass through the origin. For a rectangular or equilateral hyperbola, one whose asymptotes are perpendicular, there is an alternative standard form in which the ...
In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] + + =, where the variable x represents an unknown number, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
The standard method for computing a parametric form of the solution is to use Gaussian elimination for computing a reduced row echelon form of the augmented matrix. Then the unknowns that can be used as parameters are the ones that correspond to columns not containing any leading entry (that is the left most non zero entry in a row or the ...
An alternative approach that uses the matrix form of the quadratic equation is based on the fact that when the center is the origin of the coordinate system, there are no linear terms in the equation. Any translation to a coordinate origin (x 0, y 0), using x* = x – x 0, y* = y − y 0 gives rise to
In mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas).In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids.
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