I want the detailed knowledge of quadratic function, and then add exercises with answers (otherwise I don't know right or wrong)~

A quadratic function is a polynomial function of which the highest degree of the unknown is quadratic. A quadratic function can be expressed as f (x) = ax ^ 2 + BX + C (a is not 0). Its image is a parabola whose principal axis is parallel to the Y axis. Generally, there is the following relationship between the independent variable x and the dependent variable y: general formula: 1: y = ax

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1. For example, if the graph is a graph of quadratic function, the equation AX2 + BX + C = 3 of X follows? The graph is the axis of symmetry, and the ordinates are 3, A0, C > 0
2. Given the image over total a (- 1,0), B (3,0), C (1,8) of quadratic function f (x)
3. Given the image of quadratic function f (x) over a (- 1,0), B (3,0), C (1, - 8) To find the analytical formula, I calculate that f (x) = 2x ^ 2-4x-6. It's wrong to simplify x ^ 2-2x-3. What's the matter
4. The image of a given quadratic function f (x) passes through a (- 1,0) B (3,0) C (1, - 8) (1) find the analytic expression of F (x) (2) find the solution set of inequality f (x) ≥ 0
5. Given that f (x) is a quadratic function and the image passes through a (2. - 3), B (- 2. - 7) and C (0. - 3), what is the analytic expression of F (x)
6. The image of quadratic function passes through three points a (1 / 2,3 / 4), B (- 1,3), C (2,3),
7. We know that the image of quadratic function passes through three points a (1,3) B (- 1,5) C (2, - 1) I can't do my homework... Help me...
8. A quadratic function image through a (- 1.0) B (0.5) C (4.5) (1) find the analytic expression of quadratic function (2) find the quadratic function A quadratic function image passes a (- 1.0) B (0.5) C (4.5) (1) Finding the analytic expression of quadratic function (2) Finding the axis of symmetry and vertex coordinates of quadratic function (3) According to the image to answer what value x takes when x ≥ 0 (the image is three coordinates)
9. The image of quadratic function is known to pass through points a (1 / 2,3 / 4), B (- 1,3), C (2,3), and its analytical formula is______ ?
10. How to judge whether a, B and C in quadratic function image are greater than or less than or equal to 0
11. The image of quadratic function in junior high school mathematics The image of quadratic function y = ax & # 178; + BX + C passes through the opening of (1,0) and (0,1), and the symmetry axis is on the left side of y-axis, and the minimum value of a & # 178; + B is obtained
12. Junior high school mathematics on the image of quadratic function urgent! A rectangular grassland is 10 meters long and 8 meters wide. Now build two intersecting (Note: not vertical) paths x meters wide. At this time, the lawn area is y square meters. Find the functional relationship between X and Y. (two ends of one path are in width, and two ends of the other path are in length) Please write down the calculation process! Thank you
13. A quadratic function knows how to find an expression for an image
14. Finding the analytic expression of quadratic function （-1,0),(3,0),(1,-5) How can I get the analytic expression
15. Several analytic expressions of mathematical quadratic function What general form, vertex form and so on. Be clear
16. The undetermined coefficient method is used to find the analytic expression of quadratic function. According to the known conditions, what kinds of methods are usually used?
17. How many ways can we get the analytic expression of quadratic function? The analytic formula of quadratic function is as follows General form: y = ax ^ 2 + BX + C Vertex formula: y = a (X-H) ^ 2 + L (vertex is (h, l)) Two formulas: y = a (x-x1) (x-x2) Are the last two ideas right? Are there any other ideas?
18. What is the existence of quadratic function
19. Find the analytic expression of quadratic function according to the condition (1) The parabola passes three points (- 1, - 22), (0, - 8), (2,8) (2) The parabola passes through (- 1,0) (3,0) (1, - 5) three points (3) the length of the line segment cut by the parabola on the X axis is 4, and the vertex coordinates are (3, - 2) (4) the image of quadratic function passes through (- 1,0) (3,0) and the maximum value is 3. Where can we start
20. The analytic expressions (1) of quadratic functions are obtained respectively. The image of quadratic functions passes through points (- 1,0), (1,2), (0,3) (1) The image of the quadratic function passes through the points (- 1,0), (1,2), (0,3); (2) the vertex coordinates of the image of the quadratic function are (- 3,6) and pass through (- 2,10); (3) the intersection coordinates of the image of the quadratic function and the X axis are (- 1,0) and (3,0), and the intersection coordinates of the image of the quadratic function and the Y axis are (0,9)