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

the anwser to this problem is 2

Answer 2

Answer:

There are two x-intercepts.

Explanation:

A quadratic function whose maximum degree two. Therefore, Total two x-intercept possible.

We are given the range of quadratic function y less than equal to 2. It means parabola is downward whose maximum value 2.

Here y is greater than 2 and parabola form downward. Here must be two x-intercept.

$y=ax^2+bx+c$

If a>0 then form open up parabola.

If a<0 then open down parabola.

Here open down parabola. So, we get total two x-intercept.

Please see the attachment for diagram.