Search results
Results From The WOW.Com Content Network
Suppose a system of Cartesian coordinates is used such that the vertex of the parabola is at the origin, and the axis of symmetry is the y axis. The parabola opens upward. It is shown elsewhere in this article that the equation of the parabola is 4fy = x 2, where f is the focal length.
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 = + + into
Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [ 1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 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.
Paraboloid. In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a parabola.
The equation can be determined in this case as follows: [56] Relabel if necessary so that P 1 is to the left of P 2 and let H be the horizontal and v be the vertical distance from P 1 to P 2. Translate the axes so that the vertex of the catenary lies on the y-axis and its height a is adjusted so the catenary satisfies the standard equation of ...
Define b by the equations c 2 = a 2 − b 2 for an ellipse and c 2 = a 2 + b 2 for a hyperbola. For a circle, c = 0 so a 2 = b 2, with radius r = a = b. 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 ...
Hyperbola. A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case. Hyperbola (red): features. In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its ...