To determine which of the provided options cannot be used to write a quadratic function, let's analyze each option in detail.
1. A written description:
- A quadratic function can be described in words. For example, one might describe the function [tex]\( f(x) = x^2 + 3x + 2 \)[/tex] by stating: "The function is a polynomial of degree 2 with a leading coefficient of 1, a linear coefficient of 3, and a constant term of 2."
- Hence, a written description is a valid method to represent a quadratic function.
2. A graph:
- The graph of a quadratic function is a parabola. By analyzing the graph, one can determine important features such as the vertex, axis of symmetry, and direction (upward or downward opening). From these features, the quadratic equation can be constructed.
- Hence, a graph is a valid method to represent a quadratic function.
3. A formula:
- Quadratic functions are traditionally expressed in the form [tex]\( f(x) = ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants. Using this formula, one can clearly define the quadratic relationship.
- Hence, a formula is a valid method to represent a quadratic function.
4. A table of values:
- A table of values lists specific input-output pairs (x, f(x)) for the function. By examining the pattern and the differences between values, one can deduce the quadratic nature of the function and construct the quadratic equation.
- Hence, a table of values is a valid method to represent a quadratic function.
Given that a quadratic function can be written as a written description, a graph, a formula, or a table of values, none of these options are invalid.
Thus, the answer is that each of these options can be used to represent a quadratic function.
