How to determine the ABC of quadratic function?

Take y = ax ^ 2 + BX + C as an example, a & gt; 0 opening up a = 0 straight line a & lt; 0 opening down B and a have the same sign 1) if the condition given by the topic is the coordinates of points on the image, use the undetermined coefficient method to find the value of ABC: 2)

Quadratic function, judge positive and negative!
It's 2A + B, 2a-b. why should we compare it with - 1, 1, and the axis of symmetry? Anyway, how can we judge the positive and negative,

The general expression of quadratic function: y = ax ^ 2 + BX + C
If a > 0, the opening of parabola is upward; if a < 0, the opening is downward
X = - B / (2a) is a formula for finding the symmetry axis of quadratic function image
C is the ordinate of the intersection of function image and Y axis

How to judge the positive and negative of B of quadratic function?

Quadratic function y = ax ^ 2 + BX + C, after formula, y = a (x + B / 2a) ^ 2 + (4ac-b ^ 2) / 4ac is determined according to the position of symmetry axis X = - B / 2a of function image and the value of A

What is the relationship between the positive and negative of B and C in quadratic function and image
AX2 + BX + C = 0, according to the image how to judge B is greater than 0 or less than 0, how to judge C is greater than 0 or less than 0

If the opening is upward, then a > 0, if the opening is downward, then A0, if it intersects the lower half axis, then C0, and then determine the value of B according to the value of A. on the contrary, if the axis of symmetry is in the negative half axis of X axis, then - B / 4A

How to distinguish the positive and negative of ABC in quadratic function?

If the opening is upward, a is positive; otherwise, a is negative; if the intersection point with y axis is in the positive half axis, C is positive; otherwise, C is negative; if the symmetry axis X = B / (- 2A), judge the positive and negative of B according to him
Not to score, just give a good comment

If the image of a quadratic function passes through points (0, - 1), (- 2,0) and (4,0), the expression of the quadratic function is

y=1/8xfang-1/4x-1

Given that the image of a quadratic function passes through the coordinate origin, its vertex coordinates are (1, - 2)

Let the relation of the quadratic function be y = a (x-1) 2-2, ∵ the image of the quadratic function passes through the origin of the coordinate, ∵ 0 = a (0-1) 2-2, the solution is a = 2, so the relation of the quadratic function is y = 2 (x-1) 2-2, that is, y = 2x2-4x

How to find the interpretative expression of quadratic function?
I've learned three
One is to substitute three coordinates with the general formula y = ax ^ 2 + BX + C, which is more troublesome
I don't understand it
There is also a kind of ～ forget not to attend class ～
It's better to give some examples

Vertex type:
The vertex formula of y = ax ^ 2 + BX + C can be written as:
y=a(x+b/2a)^2+（4ac-b^2）/4a
So the vertex is (- B / 2a, (4ac-b ^ 2) / 4A)
When I tell you the vertex, and then I give you a point, or an axis of symmetry, you will know the analytic formula
For example, it is known that the vertex of quadratic function is (1,2) and passes through (2,3)
The solution can be set as
y=k(x-1)^2+2
Substitution point (2,3), k = 1
So y = (x-1) ^ 2 + 2
The third is to tell you about the point (x1,0) (x2,0). And another point
Then you can set it to
y=k(x-x1)(x-x2)
Then the third point is substituted to find the analytical formula
——————————————————————————————
Because, over point (x1,0) (x2,0)
So obviously, X1 and X2 are two parts of the equation AX ^ 2 + BX + C = 0
Ax ^ 2 + BX + C can be decomposed into K (x-x1) (x-x2)
So substituting the third point, we can get the analytical formula
For example, it is known that the vertex of quadratic function is (1,0) (2,0) and passes through point (3,2)
The solution can be set as
y=k(x-1)（x-2)
Substitution point (3,2), k = 1
So y = x ^ 2-3x + 2
Or tell you the y-axis intercept, the axis of symmetry, a point, and so on, there are many cases, but it is easy to solve the problem by remembering its vertex, the axis of symmetry, and so on

The meaning of quadratic function
What does B determine in y = ax ~ 2 + BX + C

B it's hard to say,
If B and a have the same sign, the symmetry axis of the image is on the left side of the Y axis, and the different sign is on the right side
B is zero, and the axis of symmetry is the Y axis

Who knows the definition of quadratic function?

In general, the relationship between the independent variable x and the dependent variable y is as follows: y = ax & # 178; + BX + C (a ≠ 0, C is constant), then y is called the quadratic function of X

How to determine the ABC of quadratic function?