how to find domain and range of a quadratic function

Sure, here are the steps to find the domain and range of a quadratic function:

1. Identify the quadratic function: A quadratic function is a function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and a ≠ 0.

2. Find the domain: The domain of a quadratic function is all real numbers. This is because a quadratic function is defined for all x-values. So, the domain is (-∞, ∞).

3. Find the range: The range of a quadratic function depends on the direction of the parabola (which is determined by the sign of 'a') and the vertex of the parabola.

   • If the parabola opens upwards (a > 0), the range is [k, ∞), where k is the y-coordinate of the vertex.
   • If the parabola opens downwards (a < 0), the range is (-∞, k], where k is the y-coordinate of the vertex.

4. Find the vertex: The x-coordinate of the vertex can be found using the formula -b/2a. Substitute this value into the function to find the y-coordinate.

5. Determine the range: Based on the direction of the parabola and the y-coordinate of the vertex, determine the range of the function.