The number of x-intercepts of a quadratic function with specific domain and range criteria is explained by the discriminant.
The number of x-intercepts of a quadratic function with a domain of all real numbers and a range of y ≤ 2 depends on the discriminant of the quadratic equation.
A quadratic function with a range where y ≤ 2 indicates that the graph of the function does not go above y = 2. This means the discriminant of the quadratic equation is less than zero since the quadratic formula used to find the roots involves the discriminant.
If the discriminant is negative, the quadratic function does not intersect the x-axis. Therefore, the function does not have any x-intercepts in this case.
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