In math, a vertex of a parabola is a point where the parabola intersects its axis of symmetry. The vertex is also the point where the parabola makes its sharpest turn, and it is either the minimum point for a parabola that opens upwards or the maximum point for a parabola that opens downwards. To find the vertex of a parabola, there are different methods depending on the form of the equation. Here are some common methods:
-
General Form: If the equation of the parabola is in the form y = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b/2a. After finding the x-coordinate, substitute it into the equation to find the y-coordinate of the vertex.
-
Standard Form: If the equation of the parabola is in the form y = a(x-h)^2 + k, the vertex is at the point (h, k) .
-
Vertex Form: If the equation of the parabola is in the form y = a(x - h)^2 + k or x = a(y - k)^2 + h, the vertex is at the point (h, k) .
To summarize, the vertex of a parabola is a point where the parabola intersects its axis of symmetry, and it is either the minimum or maximum point depending on the direction of the parabola. The vertex can be found using different methods depending on the form of the equation.
