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 ≤ 2. how many x - intercepts does the function have?
Answer
Explanation:
Step1: Recall quadratic - function properties
A quadratic function is of the form $y = ax^{2}+bx + c$, and its graph is a parabola. The range $y\leq2$ indicates that the parabola opens downwards (since the maximum value of $y$ is 2), so $a<0$.
Step2: Analyze x - intercepts
The x - intercepts of a function are the values of $x$ for which $y = 0$. Since the parabola opens downwards ($a < 0$) and the maximum value of $y$ is 2 (above the $x$ - axis where $y = 0$), the parabola will cross the $x$ - axis at two points.
Answer:
2