determining the number of x - intercepts\nthe domain of a quadratic function is all real numbers and the…

determining the number of x - intercepts\nthe domain of a quadratic function is all real numbers and the range is ( y leq 2 ). how many x - intercepts does the function have?

determining the number of x - intercepts\nthe domain of a quadratic function is all real numbers and the range is ( y leq 2 ). how many x - intercepts does the function have?

Answer

Explanation:

Step1: Analyze the quadratic function properties

A quadratic function (y = ax^{2}+bx + c) ((a\neq0)) has domain all real numbers. The range (y\leq2) indicates that the parabola opens downwards ((a<0)) and the vertex (y)-coordinate is (2).

Step2: Consider the (x)-intercepts

The (x)-intercepts occur when (y = 0). Since the parabola opens downwards ((a<0)) and the maximum value of (y) is (2) ((y = 2) at the vertex), and (0<2), the parabola will cross the (x)-axis at two distinct points.

Answer:

(2)