A quadratic function knows how to find an expression for an image
General form
Y = ax & # 178; + BX + C (a ≠ 0, a, B, C are constants), vertex coordinates (- B / 2a, 4ac-b & # 178 / 4A)
Vertex type
Y = a (X-H) ^ 2 + K (a ≠ 0, a, h, K are constants), vertex coordinate is (h, K), symmetry axis is x = h,
Algebra.
Two points on the x-axis are the roots of the general equation
The axis of symmetry is x = B / - 2A, which is also an algebra
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- 1. 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
- 2. 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
- 3. I want the detailed knowledge of quadratic function, and then add exercises with answers (otherwise I don't know right or wrong)~
- 4. 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
- 5. Given the image over total a (- 1,0), B (3,0), C (1,8) of quadratic function f (x)
- 6. 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
- 7. 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
- 8. 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)
- 9. The image of quadratic function passes through three points a (1 / 2,3 / 4), B (- 1,3), C (2,3),
- 10. 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...
- 11. Finding the analytic expression of quadratic function (-1,0),(3,0),(1,-5) How can I get the analytic expression
- 12. Several analytic expressions of mathematical quadratic function What general form, vertex form and so on. Be clear
- 13. 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?
- 14. 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?
- 15. What is the existence of quadratic function
- 16. 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
- 17. 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)
- 18. 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)
- 19. 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
- 20. 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