Question

Using Interval Notation, state the Domain of any quadratic function, and explain in your own words why we know this to be true.

a) (−[infinity],[infinity]); Quadratic functions extend infinitely in both directions.

b) [0,[infinity]); Quadratic functions start from zero and go indefinitely.

c) (−[infinity],0]; Quadratic functions are negative for all values.

d) [0,1]; Quadratic functions are limited to the interval [0, 1].

Answer 1

The domain of any quadratic function is (-∞, ∞), as they are defined for all real values of 'x' and extend infinitely in both directions on the x-axis.

Step-by-step explanation:

The domain of any quadratic function is (-∞, ∞), which in interval notation is written as (-∞, ∞). This is because quadratic functions, which are mathematical functions known as second-order polynomials, are defined for all real values of 'x'. A quadratic function typically has the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. For any real value of 'x', you can substitute it into the function and get a corresponding real number 'y'. Hence, quadratic functions do not have any restrictions on their domains and they extend infinitely in both the positive and negative directions of the x-axis.