Current location - Training Enrollment Network - Mathematics courses - The Mathematical Problem of a Quadratic Function
The Mathematical Problem of a Quadratic Function
1 m=3 The characteristic number is (-6,4,2).

a=-6 b=4 c=2

(-b/2a, 4ac-b2/4a) vertex coordinates are x =-b/2a =1/3y = 4ac-b2/4a = 8/3.

1 is correct.

2 when m> is at 0 o'clock; x 1+x2 =-b/a = m- 1/m x 1 * x2 =- 1-m/2m

(x 1-x2)^2=(x 1+x2)^2-4x 1x2=9/4+6/4m+ 1/4m^2

|x 1-x2| > Under the radical sign (9/4)=3/2

2 correct

3. When M

x =-b/2a = m- 1/4m = 1/4- 1/4m

X> 1/4- 1/4m is a decreasing function.

So x> is at 1/4, and y decreases with the increase of x.

3 correct

When m≠0, the function passes through the same point.

△=b^2-4ac=(m- 1)^2+8m(m+ 1)=9m^2+6m+ 1

=(3m+ 1)^2

So 4 is correct.