Question

Quadratic equations can yield two solutions for x, but the function itself has a single output. Which of the following statements correctly explains this apparent contradiction?

a) Quadratic equations always violate the rule of one output value for a function.

b) Each solution of a quadratic equation represents a distinct function.

c) The rule applies to functions as a whole, not individual equations.

d) The rule is a generalization and doesn't hold true in all cases.

Answer 1

The apparent contradiction in quadratic equations is explained by the fact that the rule of one output value for a function applies to functions as a whole, not individual equations. Each solution of a quadratic equation represents a distinct function.

Step-by-step explanation:

The correct explanation for the apparent contradiction in quadratic equations is that the rule of one output value for a function applies to functions as a whole, not individual equations. Each solution of a quadratic equation represents a distinct function. When we solve a quadratic equation, we are finding the x-values at which the quadratic function crosses the x-axis. These x-values are the roots of the equation and represent the inputs that result in a zero output for the function.