###### Answer: The focus is located at (0 -3)The parabola can be represented by the equation x^2 = -12y Government Midterm 1

In mathematics a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.It fits several superficially different mathematical descriptions which can all be proved to define exactly the same curves.. One description of a parabola involves a point (the focus) and a line (the directrix ).The focus does not lie on the directrix . The parabola is the locus of points in …

This is extremely easy to verify in coordinates: dilating the parabola y =ax^2 by R gives y /R = a(x/R)^2 which has exactly the same effect as the result of scaling the parameter a by 1/R or scaling along the y -axis by 1/R or scaling along the x-axis by the square root of R. –JBL 16:30 16 August 2015 (UTC) I realize all that. But a figure …

Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange). Its x-intercepts are rotated 90° around their mid-point and the Cartesian plane is interpreted as the complex plane (green). The function f(x) = ax 2 + bx + c is a quadratic function. The graph of any quadratic function has the same general shape …

For example a univariate (single-variable) quadratic function has the form = + + ≠in the single variable x.The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y -axis as shown at right.. If the quadratic function is set equal to zero then the result is a quadratic equation.The solutions to the univariate equation are called the roots of the …

Thus it is the distance from the center to either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction keeping fixed. Thus a and b tend to infinity a faster than b. The major and minor axes are the ax…