Search results
Important Notes on Vertex of a Parabola: The vertex of a parabola f(x) = ax 2 + bx + c is (-b/2a, f(-b/2a)). Its axis of symmetry is x = -b/2a. Instead of using the formula x = -b/2a, we can convert the standard form f(x) = ax 2 + bx + c into vertex form f(x) = a (x - h) 2 + k by completing the square to find the vertex (h, k).
The equations of parabolas with vertex \((0,0)\) are \(y^2=4px\) when the x-axis is the axis of symmetry and \(x^2=4py\) when the y-axis is the axis of symmetry. These standard forms are given below, along with their general graphs and key features.
Completing the Square. If a quadratic function is given in vertex form, it is a simple matter to sketch the parabola represented by the equation. For example, consider the quadratic function. f(x) = (x + 2)2 + 3. which is in vertex form. The graph of this equation is a parabola that opens upward.
Determine the vertex of a parabola by utilizing the Vertex Form. Learn the skills to express the parabola's equation algebraically in vertex form, when the vertex is specified and if the y-intercept or any point along the parabola is given.
Vertex form of a parabola. To find the vertex given an equation in vertex form f(x) = a(x - h) 2 + k, just find (h, k). The vertex is located at the point (h, k). Just be careful with the signs in the equation. Standard form of a parabola. To find the vertex given the standard equation of a parabola, (x - h) 2 = 4p(y - k), just find (h, k). The ...
If a is positive, the parabola open up and will have a minimum point at the vertex. If a is negative, the parabola open down and will have a maximum point at the vertex. If |a| > 1 , it will have a "skinny" parabola comparing to y=x² If |a| < 1, it will have a "fat" parabola comparing to y=x²
The form of the quadratic function f(x) = a(x − h)2 + k is called vertex form. The graph of this quadratic function is a parabola. The graph of the parabola opens upward if a > 0, downward if a < 0. If the magnitude of a is larger than 1, then the graph of the parabola is stretched by a factor of a.
