Answer:
The condition of a ≠ 0 is imposed in the definition of the quadratic function to ensure that the function represents a true quadratic equation.
In a quadratic function of the form f(x) = ax^2 + bx + c, the coefficient "a" represents the leading coefficient or the coefficient of the quadratic term. This coefficient determines the shape of the graph and whether the function represents a quadratic equation.
When a = 0, the quadratic term becomes zero, resulting in a linear function (f(x) = bx + c) rather than a quadratic function. In other words, without the condition a ≠ 0, the function would degenerate into a straight line, losing the key characteristics and properties associated with quadratic equations, such as the presence of a vertex, concavity, and the ability to intersect the x-axis at most two times.
By imposing the condition a ≠ 0, we ensure that the quadratic function represents a genuine quadratic equation, allowing us to study and analyze its properties, such as the vertex, axis of symmetry, roots, and the behavior of the graph. It helps distinguish quadratic functions from linear functions and ensures that we are working with the appropriate mathematical model when dealing with quadratic relationships and phenomena.
Explanation: