Question

The domain of a quadratic function is all real numbers and the range is y ≤ 2. How many x-intercepts does the function have?

Answer 1

Answer:  2

Explanation:

The range is y ≤ 2 which means that y = 2 is the largest y can get. The parabola opens downward to form a sort of "frowny face" so to speak. When moving down the parabola, we'll cross the x axis at two different spots. An example of this is shown below with the equation y = -x^2+2.

There's no connection between the '2' in y ≤ 2 and the final answer of 2 roots. We could easily have a range of something like y ≤ 5 or y ≤ 8 and the answer will still remain as 2. The most roots a parabola can have is 2.