Let f (x) = ax ^ 2 + BX + C, where a is a positive integer, B is a natural number, and C is an integer If the inequality 4x ≤ f (x) ≤ 2 (x ^ 2 + 1) holds for any real number x, and there exists x0 such that f (x0)

Middle school students~
Thinking:
In the same coordinate system to make y = 4x and y = 2 (x ^ 2 + 1) graph, this should be ~ if not, do not look down~
The graph of F (x) you requested should be within the above two. We can see that C should be between (0,2). From the title, C is an integer, so C = 1
It can also be confirmed by recalculation
C should be between (0,2), but not all of them meet the requirements
Let g (x) = 2 (x ^ 2 + 1) + K, which is a parabola with the same shape as y = 2 (x ^ 2 + 1). Find the intersection point of G (x) and the straight line y = 4x, determine the K value in G (x), and find the intersection point of G (x) and Y axis. Then between the intersection point and 2 is the value range of C. from the topic, C is an integer, so C = 1

It is known that x2-ax-24 can decompose factors in the range of integers, then the value of integer a is______ Just fill in one

By cross multiplication, then - 24 can be decomposed into 1, - 24 or - 1, 24, so a can be ± 23; similarly, it can be decomposed into - 2, 12, 2, - 12, so a can be ± 10; similarly, it can be decomposed into 3, - 8, - 3, 8, so a can be ± 5; similarly, it can be decomposed into 4, - 6, - 4, 6, so a can be ± 2

If the quadratic trinomial x2-ax + 15 can decompose factors within the range of integers, then the value of integer a is (just fill in one answer that you think is correct)______ ．

3×5=15，-a=3+5，a=-8．

Let f (x) = ax ^ 2 + BX + C, where a is a positive integer, B is a natural number, and C is an integer If the inequality 4x ≤ f (x) ≤ 2 (x ^ 2 + 1) holds for any real number x, and there exists x0 such that f (x0)