Find the analytic expression of this quadratic function When the input value is x, the input value is y, and Y is a quadratic function of X. when the input value is - 2,0,1, the corresponding output values are 5, - 3, - 4, respectively. Find the analytic expression of the quadratic function

Find the analytic expression of this quadratic function When the input value is x, the input value is y, and Y is a quadratic function of X. when the input value is - 2,0,1, the corresponding output values are 5, - 3, - 4, respectively. Find the analytic expression of the quadratic function

Let the analytic expression of this quadratic function be: y = ax & sup2; + BX + C
When x = - 2, y = 5
When x = 0, y = - 3
When x = 1, y = - 4
Then: 5 = 4a-2b + C
-3=c
-4=a+b+c
So 4a-2b = 8
a+b=-1
a=1
Substituting a = 1 into a + B = - 1, we get the following result:
1+b=-1
b=-2
∴ a=1
b=-2
c=-3
The analytic formula is: y = x & sup2; - 2x-3

Excuse me, how to find an analytic expression when solving quadratic function and how to set an analytic expression

If the coordinates of three points are known, let y = ax & # 178; + BX + C
If the vertex is known, let y = a (X-H) &# 178; + K
If two intersections with X axis are known, let y = a (x-x1) (x-x2)

The analytic expression of quadratic function of one variable
The image of quadratic function f (x) of one variable passes through P (0, - 2), and the analytic expression of F (x) is obtained
Let f (x) = a (x-1) ^ 2 + 2
Point passing P (0, - 2)
a(0-1)^2+2=-2
a=-4
Analytical formula: F (x) = - 4 (x-1) ^ 2 + 2
Please help me correct my mistakes

Right

I want to use matlab to draw the image of a function obtained by dividing two quadratic functions, please give an example

syms x;
y=(x+1)^2-4;
z=(2*x-4)^2+5;
ezplot(y/z)

The problem of quadratic function of one variable
It is known that the two roots of the quadratic function equation of one variable ax & sup2; + BX + C = 0 are X1 = - 2 and X2 = - 3. Then the intersection of the parabola y = ax & sup2; + BX + C and the X axis is______ .

(-2,0) (-3,0)

Two solutions to the value of quadratic function of one variable
1. Given that the quadratic function of one variable y = x ^ 2 + ax + 2x + 3 is an increasing function in the interval [- 2, + ∞), then the value range of real number a is
2. Given that the quadratic function of one variable y = x ^ 2 + (m-2) x + 1 is a decreasing function in the interval (- ∞, 2), then the value range of real number m is

A:
1）
y=x^2+ax+2x+3
=x^2+(a+2)x+3
The opening of parabola is upward, and the axis of symmetry x = - (a + 2) / 2
Because: when x > = - 2, y is an increasing function
So: axis of symmetry x = - (a + 2) / 2 = 2
2）
y=x^2+(m-2)x+1
The opening of parabola is upward, and the axis of symmetry x = - (m-2) / 2
Because: x = 2
The solution is: M

The problem of quadratic function of one variable in junior high school
Given that the image of quadratic function y = a ^ 2 + BX + C passes through point (C, 2), and a | a | + B | B | = 0, the inequality a ^ 2 + BX + C-2 > 0 has no solution, try to find the analytic expression of quadratic function y = a ^ 2 + BX + C

There are images (in imagination) that can be seen: a

It's a headache to see quadratic function
General problems can be solved
But the final question has not changed a bit
One question costs a lot of time

It is suggested that you do more questions about quadratic function. At the beginning, you can refer to the answers. When you do more, you can find some rules. At this time, you can solve the problems independently. In short, you can do more quadratic function problems. This kind of problems are generally three questions, one is to find the analytic formula, two is to find the maximum value, three is to find the special point, which is a little troublesome Need a lot of practice to get the experience of doing the problem, you can try it. This is how I do the quadratic function

Image problems of quadratic function
It is known that the function y = 4x / 5-24x / 5 + 4 passes through point a (0,4) point B (1,0) point C (5,0), and the parabola symmetry axis L and X axis intersect at point m (3,0)
Connecting AC, is there a point n on the parabola below the straight line AC, so that the area of the triangle NAC is the largest? If so, the coordinates of point n can be obtained
(just this question. The previous energy saving is all saved. MS is at the top of the parabola,

The analytic formula of the straight line AC is: y = - 4x / 5 + 4. Whether there is a point n on the parabola below the straight line AC, so that the area of the triangle NAC is the largest, that is, when the straight line AC moves down to only one intersection (tangent) with the parabola, the height is the largest, and the area is the largest. At this time, the discriminant of the parabolic and linear equations is 0

Quadratic function image problem, urgent 40 points
Given quadratic function y = ax square + BX + C, 0 ＜ - B / 2A ＜ 1, a ＜ 0, B ＞ 0, C ＞ 0, when x = - 1, y ＜ 0, when x = 2, y ＞ 0, prove a + C ＞ 0

The symmetry axis of F (x) is between 0 and 1, and its image is a parabola with an opening downward
From F (- 1) 0, - B / 2A - (- 1) > 2 - (- B / 2a),
So B0
Due to a