What is how to find the vertex?

The vertex of a parabola is a crucial point representing either its maximum or minimum value. Finding the vertex depends on how the quadratic function is presented. Here's a breakdown:

• Standard Form: If your quadratic function is in the form f(x) = ax² + bx + c, you can find the x-coordinate of the vertex using the formula: x = -b / 2a. Then, substitute this x-value back into the original equation to find the corresponding y-coordinate, giving you the vertex (x, y). The link for the formula is: x = -b / 2a

• Vertex Form: If your quadratic function is in the vertex form f(x) = a(x - h)² + k, the vertex is simply the point (h, k). Note that the x-coordinate is the opposite of the value inside the parenthesis. The link for the vertex form is: Vertex Form

• Factored Form: If your quadratic is in factored form, f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots (x-intercepts) of the equation, the x-coordinate of the vertex is the average of the roots: x = (r₁ + r₂) / 2. Then, substitute this x-value back into the original equation to find the y-coordinate.The link for the Factored form is: Factored Form

Once you have the vertex coordinates, you know either the maximum or minimum point of the parabola. If a > 0, the parabola opens upwards and the vertex represents the minimum value. If a < 0, the parabola opens downwards and the vertex represents the maximum value. The link for a value is: a value