![]() To convert a parabola in vertex form to standard form, expand the equation and simplify. Then, a is the same in both forms, so simply copy that to the vertex form equation. Equations Inequalities System of Equations System of Inequalities. Plug these values in for h and k in the vertex form equation. Free Parabola calculator - Calculate parabola foci, vertices, axis and directrix step-by-step. The x-value of the vertex is x = -, so the y-value is y = f ( - ). You can also convert to vertex form by using the knowledge that the vertex lies on the axis of symmetry. Vertical Parabola (Standard Equation) - calculator - fx Solver Vertical Parabola (Standard Equation) Add to Solver Description Parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped but which can be in any orientation in its plane. You can use completing the square to convert a quadratic in standard form into vertex form. ![]() The standard equation of a regular parabola is y 2 4ax. Now all that has to be done is to plug in points around the vertex, then graph. The general equation of a parabola is: y a (x-h) 2 + k or x a (y-k) 2 +h, where (h,k) denotes the vertex. Vertex form makes it much easier to graph a parabola because it makes it easy to plot the vertex.įrom this equation, we can already tell that the vertex of the parabola is at ( 1,4), and the axis of symmetry is at x = 1. Vertex form is very similar to the general expression for function transformations. In vertex form, ( h,k) describes the vertex of the parabola and the parabola has a line of symmetry x = h. If a is negative, the parabola will open downwards. If a is positive, the parabola will open upwards. The a in the vertex form of a parabola corresponds to the a in standard form. The vertex form of a parabola is another form of the quadratic function f(x) = ax 2 + bx + c. The axis of symmetry is located at y = k. The focus of parabolas in this form have a focus located at ( h +, k) and a directrix at x = h. For horizontal parabolas, the vertex is x = a(y - k) 2 + h, where (h,k) is the vertex.
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