What is how to find vertex?

Finding the Vertex of a Parabola

The vertex of a parabola is the point where the parabola changes direction. It is either the minimum or maximum point of the parabola. Knowing how to find the vertex is crucial for understanding and analyzing quadratic functions.

There are a couple of common methods to find the vertex:

1. Using the Vertex Form:

   • If the quadratic equation is given in vertex form, which is: y = a(x - h)^2 + k where (h, k) represents the coordinates of the vertex. Simply identify the values of h and k. Note that the x-coordinate of the vertex (h) has the opposite sign of what appears inside the parentheses.

2. Using the Formula:

   • If the quadratic equation is given in standard form: y = ax^2 + bx + c
   • The x-coordinate of the vertex can be found using the formula: x = -b / 2a
   • Once you have the x-coordinate, substitute it back into the original equation to find the y-coordinate. This gives you the y-coordinate of the vertex. The vertex is (x, y) or (-b/2a, f(-b/2a)).

3. Completing the Square:

   • This method transforms the standard form equation into vertex form. It involves algebraic manipulation to create a perfect square trinomial. See a guide about completing%20the%20square.

Important Considerations:

• The coefficient a in the quadratic equation determines whether the parabola opens upward (a > 0, vertex is a minimum) or downward (a < 0, vertex is a maximum). If a = 0, the equation is not a parabola.
• The vertex represents the axis%20of%20symmetry of the parabola. The vertical line that passes through the vertex.