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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. At the positive x end of the chord, x = c / 2 and y ...
Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. 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.
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.
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.
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
Vertex (curve) An ellipse (red) and its (blue). The dots are the vertices of the curve, each corresponding to a cusp on the evolute. In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. [1] This is typically a local maximum or minimum of curvature, [2] and some authors define a vertex to be ...
Cubic equation. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0 ). The case shown has two critical points. Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero.