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?

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• 1. Several analytic expressions of mathematical quadratic function What general form, vertex form and so on. Be clear
• 2. Finding the analytic expression of quadratic function （-1,0),(3,0),(1,-5) How can I get the analytic expression
• 3. A quadratic function knows how to find an expression for an image
• 4. 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
• 5. 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
• 6. I want the detailed knowledge of quadratic function, and then add exercises with answers (otherwise I don't know right or wrong)~
• 7. 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
• 8. Given the image over total a (- 1,0), B (3,0), C (1,8) of quadratic function f (x)
• 9. 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
• 10. 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
• 11. 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?
• 12. What is the existence of quadratic function
• 13. 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
• 14. 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)
• 15. According to the following conditions, the analytic expressions of quadratic functions are obtained respectively (1) It is known that the image of quadratic function passes through the point (- 2, - 1), and when x = - 1, the function has the maximum value of 2; (2) It is known that the symmetry axis of quadratic function image is a straight line x = 1, which intersects the coordinate axis at points (0, - 1), (- 1,0)
• 16. The analytic expression of quadratic function is obtained according to the given conditions 1 image passes through (1,0), (negative 1,4) and (0,3) 2. The vertex of the image is (2, negative 1) and passes through (0, 3); The intersection points of 3 images on the horizontal axis are (negative 1,0), (3,0) and have a maximum value of 4
• 17. As shown in the figure, we know that the image of quadratic function y = X2 - (M-3) x-m is a parabola. (1) when we try to find the value of M, the distance between the two intersections of parabola and x-axis is 3? (2) When m is the value, the two roots of the equation X2 - (M-3) x-m = 0 are negative? (3) Let m be the vertex of the parabola and P, Q be the intersection point of the parabola and x-axis
• 18. Master of mathematics, please come in (quadratic function) 1. State the opening direction, axis of symmetry and vertex coordinates of the following parabola ⑴,y=1/3(x-5/3)^2+2/3 ⑵,y=-0.7(x+1.2)^2-2.1 ⑶,y=15(x+10)^2+20 ⑷,y=-1/4(x-1/2)^2-3/4 2. The following functions are reduced to the form of y = a (X-H) ^ 2 by the collocation method (1)y=x^2+4+5 (2)y=2x^2+4x 3. The vertex coordinates of parabola y = - 12x2 + 2x + 4 are_______ The axis of symmetry is_______ ； 4. The maximum value of quadratic function y = AX2 + 4x + A is 3, and the value of a is obtained 5. If the coordinates of any three points on the image of a quadratic function are known, the general formula (a ≠ 0) is used to find the analytic formula 6. Given the parabola y = 4 (x-3) ^ 2-16, write its opening direction, axis of symmetry and vertex coordinates 7. Determine the opening direction of parabola according to vertex formula__ The axis of symmetry is____ The vertex coordinates are____ .
• 19. Mathematical quadratic function + circle. Teach me In the same rectangular coordinate system, it is known that the parabola y = 1 / 4x ^ - x + K intersects the Y axis at B (0,1), the point C (m, n) is on the parabola, and the circle m with diameter BC just passes through vertex a The value of K is 1 2. Find the value of point C What is vector theorem? How did (m-2, n) * (- 2, 1) come from
• 20. If one root of the equation MX & # 178; - 2x + 1 = 0 is in the interval (0,1) and the other root is in the interval (1,2), find the value range of the real number M,