Quadratic inequality of one variable in mathematics of grade one of senior high school When m takes any value, the quadratic inequality MX ^ 2 + (m-1) x + m < 1 holds for any real number X

Quadratic inequality of one variable in mathematics of grade one of senior high school When m takes any value, the quadratic inequality MX ^ 2 + (m-1) x + m < 1 holds for any real number X

Transfer, get
mx²+(m-1)x+(m-1)

Given that the solution set of inequality ax & sup2; + BX + C ＞ 0 is {x | - 1 / 3 ＜ x ＜ 2}, find the solution set of inequality CX & sup2; + BX + a ＜ 0

First of all, a

A course of solving the system of quadratic inequalities of one variable
What is the solution set of 1 + 2x / 3 > X-1?

1+2X/3>X-1
1+1>x-2X/3
2>X/3
X

Quadratic inequality of one variable and its solution
Given the function f (x) = - X & sup2; + 2x + B & sup2; + 1 (b belongs to R), if f (x) > 0 holds when x belongs to [- 1,1], then the value range of B is?

If f '(x) = - 2x + 2, when f' = 0, x = 1 is the extremum of F (x), and the interval [- ∞, 1] is a monotone increasing interval (Note: the simplest is to substitute x = 0, and the result is a positive number), where [- 1,1] belongs to [- ∞, 1]

The solution of one variable quadratic inequality system
0

4x^2-11x-3>0
(4x+1)(x-3)>0
x> 3 or X

The solution of quadratic inequality with parameter
The inequality x ^ 2 + (1-2a) x-2a > 0 holds when x 3, and the value range of a is obtained

Let f (x) = x ^ 2 + (1-2a) x-2a, whose opening is upward. To make x ^ 2 + (1-2a) x-2a > 0 hold in X3, we only need f (- 2) ≥ 0, f (3) ≥ 0, and the solution is: - 1 ≤ a ≤ 3 / 2

Solution of quadratic inequality with parameter
x2+2x-a

This kind of problem should be discussed by category
First of all, let's not consider this inequality. Let's consider a function y = x2 + 2x-a
The solution to the original problem is the part of the function below the x-axis, right
Let's first consider the value of delta = b2-4ac = 4 + 4a
If delta 0 indicates that the function has a region below the x-axis, and first solves the solutions X1 and X2 of x2 + 2x-a = 0, then the solution set is x1

How to explain the knowledge of quadratic function in the third grade of junior high school?
The symmetry axis of the square of y = ax - C, vertex?
Y = square of AX + axis of symmetry of BX, vertex?
The symmetry axis of the square of y = a (X-H), vertex?
What other parabola passing through the origin
The square of quadratic function y = x - 2x + 4 is transformed into the form of square of y = a (X-H) + k? --- 555

After reading these summaries, try again. Don't be afraid that you won't be able to do these questions. The more you are afraid, the more you can't do them!
If you try, you will find that, in fact, it's not difficult
1、 (1) general formula: y = ax ^ 2 + BX + C (a ≠ 0)
Axis of symmetry: x = - B / 2A (* Note: axis of symmetry is a straight line!)
Vertex: (- B / 2a, (4ac-b ^ 2) / 4A)
(2) Vertex formula: y = a (x-m) ^ 2 + n (a ≠ 0)
Axis of symmetry: x = m
Vertex: (m, n)
(3) Intersection formula: y = a (x-x1) (x-x2) (a ≠ 0)
2、 Image parabola
1、
Opening direction: a > 0, opening upward
a

High school quadratic function
f(X)=x^2+2ax+b(b

Analysis: 1) f (1) = 0, substituting 1 + 2A + B = 0
② F (x) + 1 = 0 has real root ∧ discriminant = 4A & sup2; - 4 (B + 1) ≥ 0
(replace a in (2) with a = - 1 - B / 2 transformed by (1))
∴b²-2b-3≥0
∴ 3=0 ）
M^2+2AM-2A=0 .1
(M-4)^2+2A(M-4)-1-2A=Y.2
The formula 2-1 is obtained
15-8M-8A
Another 0

Summary of junior high school biology knowledge points