Question

Dan said that if a quadratic equation does not have any real solutions , it is not a function . Critique his reasoning

Answer 1

Solutions of a quadratic functions are x-intercepts, or when y equals zero. A graph with its maximum (highest point) below the x-axis or a graph with its minimum (lowest point) above the x-axis never touches or crosses the x-axis, so it has no real solutions. It is still a quadratic function, as long as it has a variable to the second power (definition of quadratic) and passes the vertical line test (definition of function). 

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