Question

How to find the practical domain of a quadratic function?

a) Determine the x-values where the quadratic function is undefined.
b) Identify the vertex and use its x-coordinate as the domain.
c) Consider any restrictions imposed by the context of the problem.
d) Set the quadratic expression equal to zero and solve for x.

Answer 1

To find the practical domain of a quadratic function, you can follow these steps: determine x-values where the function is undefined, identify the vertex and use its x-coordinate as the domain, consider context restrictions, and solve the quadratic expression for x.

Step-by-step explanation:

To find the practical domain of a quadratic function, you can follow these steps:

1. Determine the x-values where the quadratic function is undefined. This includes values that would result in division by zero, such as when the quadratic function is in the denominator of a fraction.
2. Identify the vertex of the quadratic function and use its x-coordinate as the domain. The vertex is the point where the quadratic function reaches its highest or lowest value.
3. Consider any restrictions imposed by the context of the problem. For example, if the problem involves measuring time, negative values for time might not make sense.
4. Set the quadratic expression equal to zero and solve for x. This will give you the x-values where the quadratic function crosses the x-axis.