Find the analytic expression of quadratic function satisfying the following conditions: (1) the image passes through points a (0,3), B (1,3), C (- 1,1); (2) the image passes through points a (- 1,0), B (3,0), C (0,6); the image vertex coordinates are (1, - 6), and pass through points (2, - 8) Prawn, tears run ah, math children really tears ah, you can't afford to hurt ah, QAQ!

Find the analytic expression of quadratic function satisfying the following conditions: (1) the image passes through points a (0,3), B (1,3), C (- 1,1); (2) the image passes through points a (- 1,0), B (3,0), C (0,6); the image vertex coordinates are (1, - 6), and pass through points (2, - 8) Prawn, tears run ah, math children really tears ah, you can't afford to hurt ah, QAQ!

If you can't solve a system of linear equations with three variables, you'd better learn mathematics from the beginning of junior high school

On the problem of quadratic function,
Given that the image of a quadratic function passes through the origin and point (- 1 / 2, - 1 / 4), and the distance between the image and another intersection of X axis is 1, the analytic expression of the quadratic function is ()
The distance from the intersection of the image and the x-axis to the far point is 1*^__ ^*(hee hee...)

There are two cases, one is: y = ax ^ 2 + BX
One is y = - 1 / 3ax ^ 2 + 1 / 3B
It's hard to type out the process with a computer Let me give you some ideas. Just because it crosses the origin, so C is zero, and then it is substituted into (- 1 / 2, - 1 / 4) to get a binary linear expression of a and B. because the distance from the other intersection of the image and X axis to the far point is 1, there are two cases of the third point, one is (1,0), the other is (- 1,0), and then it can be calculated by taking it in separately~
If you need a more specific process Can you contact me I'll send you my draft picture
I hope I can help you~~~~~~

Given the points a (- 1,0), B (3,0), C (0, t), and t ＞ 0, Tan ∠ BAC = 3, the parabola passes through three points a, B and C, and the point P (2, m) is an intersection of the parabola and the straight line
(1) Find the analytical formula of parabola;
(2) For the moving point Q (1, n), find the minimum value of PQ + QB;
(3) If the moving point m moves on the parabola above the straight line,
Find the maximum value of high h on the side AP of △ amp
No picture But it's easy to draw

1) As shown in the figure, suppose that the analytic formula of the parabola is y = ax & sup2; + BX + C, a 〈 0, symmetric with respect to the straight line x = 1, Tan ∠ BAC = 3, Ao = 1, OC = 3, so t = 3, C (0,3) C point is on the parabola, substituting the above formula to get C = 3A, y = ax & sup2; + BX + 3 point a, B on the parabola, substituting the above formula to get A-B + 3 = 09A + 3B + 3 = 0, the solution to get a = - 1. B = 2

Given the quadratic function y = x2-x + M. (1) write out the opening direction, vertex coordinates and symmetry axis of its image; (2) try to judge: when m takes what value, the vertex of the image of the function is above the X axis; (3) if the image of the function crosses the origin, find out its function relation; and judge what value the independent variable x takes, y increases with the increase of X?

(1) The quadratic function y = x2-x + M = (X-12) 2-14 + m ∵ a > 0, the opening of the parabolic line is upward, the axis of symmetry is x = 12, and the vertex coordinates are (12, - 14 + m). (2) from the known solution, i.e. - 14 + m > 0, M > 14, (3) ∵ the quadratic function y = x2-x + m crosses the origin, ∵ M = 0, and the analytic expression of the function is y = x2-x

For knowledge, I hope you can do some quadratic function problems for me? I don't know much about quadratic function in class
5555 teacher immediately finished teaching, I did not learn

It's a parabola. There are plenty of junior high school mathematics textbooks. It's very easy for the landlord to find a book to learn by himself

What points do you need to know to draw quadratic function image?

The more points you draw, the more accurate the image will be. On the contrary, the less points you draw, the greater the error between the image and the correct image will be

What is the image of quadratic function?

a: A is divided into two parts: sign and size (i.e. absolute value) sign: a positive sign indicates that the opening is upward, and a negative sign indicates that the opening is downward. The larger the absolute value of a is, the smaller the parabolic opening is (thin). The smaller the absolute value of a is, the larger the parabolic opening is (fat). B: B can't judge alone. To judge with a, there is a formula: left

Who knows better about quadratic function
If points (2,5) (4,5) are two points on the parabola y = ax ^ 2 + BX + C, then the axis of symmetry of the parabola is a straight line x =?

Substituting (2,5) and (4,5) into y = ax ^ 2 + BX + C, we get
5=4a+2b+c
5=16a+4b+c
The solution is b = - 3a
Then y = ax ^ 2-3ax + C = a (x ^ 2-3x + 9 / 4) - 9A / 4 + C = a (x-3 / 2) ^ 2-9a / 4 + C
Obviously, the axis of symmetry is x = 1.5

Quadratic function is about ABC. For example, a + B + C reflects the size of 1. Anyway, it is the relationship between ABC and quadratic function
-Is the same sign of B / 2A negative and the different sign positive on the left and right sides of the y-axis

As long as x = 1, we can get the form of a + B + C = y, that is to say, we can find the value of y when x = 1
Yes, because x = - B / 2a is the axis of symmetry, and - B / 2a is negative. Of course, on the left side of the axis, it is right

A of quadratic function represents opening direction. What do B and C mean respectively