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Why is the vertex formula of quadratic function p (h, K)]: y = a (X-H) ^ 2 + k How did it come out?
Generally, junior high school mathematics obtains this result through formula. In senior high school mathematics, this formula can be derived with the help of derivative. For example, ax ^ 2 + BX + C = f (x) (a > 0, b > 0), then its derivative function about X is f "(x) = 2aX + B
If f "(x1) = 0 and if any x > x1, F" (x) > 0 if any x
RELATED INFORMATIONS
- 1. Is there a better introduction to the image and properties of quadratic function y = a (X-H) 2K
- 2. The analytic expression of quadratic function is y = a (x + H) ^ 2 + K or y = a (X-H) ^ 2 + K
- 3. The larger the absolute value of the quadratic coefficient, the more open the parabola is?
- 4. Is a, which can determine the opening direction of quadratic function, the same as the coefficient a of quadratic term in the general formula of quadratic function?
- 5. Why the larger the value of | a | in quadratic function, the smaller the opening
- 6. Does the maximum value problem of quadratic function contain absolute value? F (x) = the square of X + the absolute value of x-2-1 to find the minimum value of the function,
- 7. What does the value of 2A + B in quadratic function image relate to
- 8. How to determine the sign of 2A + B (2a-b) in quadratic function?
- 9. Given the image of quadratic function as shown in the figure, find the relationship between 2A + B and 0
- 10. What is the expression of a quadratic function if its image opening is downward, its vertex is (- 2,3) and it passes through the origin?
- 11. Induction: image and properties of quadratic function y = a (x + H) ² + k
- 12. Image shape of quadratic function What does the shape of the image of quadratic function have to do with? y=ax^2+bx+c
- 13. What can be explained by the same shape of quadratic function image The shape of y = ax ^ 2 + BX + C is the same as that of y = - x ^ 2-7x + 12, the symmetry axis is x = 1, and the distance from the vertex to the X axis is the root sign 3
- 14. Is the same shape of two quadratic functions the same a value?
- 15. Properties and applications of quadratic function
- 16. In quadratic function, if two parabolas have the same shape, is a the same, or is the absolute value of a the same? In other words, the same shape, the same opening direction?
- 17. What is the a value of quadratic function with the same image shape as function y = - x?
- 18. The opening direction and shape of quadratic function image and parabola y = - 2x ^ 2 are the same, x = 1, and the minimum value is - 1
- 19. It is known that the coefficients a, B and C of quadratic function y = ax ^ + BX + C are integers, and when x = 19 or x = 99, y = 1999, | C|
- 20. The intersection of the image of the quadratic function y = - x ^ 2 / 2 + X + 4 and the X axis is a and B from left to right, the intersection with the Y axis is C, and the vertex is d 1. Finding the area of quadrilateral abdc 2. Find a point d 'on the parabola in the first quadrant to maximize the area of quad abd'c