When x=0, y=0, that is 2a+3 = 0 = =>；; a=-3/2
The function y =-3/2x 2-x, the symmetry axis x=- 1/3, the opening is downward, and the monotonic increasing interval is (-∞,-1/3).
14. Let the function f (x) = x 2-(3a- 1) x+a 2 be the increasing function in the interval (1, +∞). What is the range of real number a?
F(x) increasing interval ((3a- 1)/2, +∞) ∴ (3a-1)/2 ≤1= >; 3a- 1≤2== >a≤ 1
15. If the function f(x) = (a-2) x 2+(a- 1) x+3 is an even function, what is the increasing interval of f(x)?
F(x) is an even function, then a- 1=0== >a= 1
The increasing interval of f (x) =-x 2+3 is (-∞, 0].
16. What is the domain of the function y=√ 1-log, 2(4x-5)?
1-log2(4x-5) ≥0== >log(2)(4x-5)≤ 1 == >4x-5≤2== >x≤7/4
4x-5 & gt； 0 = = >； x & gt5/4
The domain of intersection is (5/4, 7/4)
17. What are the ranges of the functions y = x (6-2x) and x ∈?
What is the range of y= 1/2*?
y=-(x^2+2x+ 1)+4=-(x+ 1)^2+4
x=- 1，ymax=4，x=0，x=-2，ymin=3
The range of values is
19. What are the ranges of the functions y = x 2-4x+3 and x ∈?
y=x^2-4x+3=(x-2)^2- 1
x=2，ymin =- 1； x=-2，ymax= 1 1
The range of values depends on the increasing function.
The decreasing interval of the original function is (1, 2).