Properties and applications of quadratic function

Quadratic function
1. Definition and definition expression
In general, the relationship between independent variable x and dependent variable y is as follows:
Y = ax ^ 2 + BX + C (a, B, C are constants, a ≠ 0, and a determines the opening direction of the function. When a > 0, the opening direction is upward, a ≠ 0

RELATED INFORMATIONS

1. Is the same shape of two quadratic functions the same a value?
2. 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
3. Image shape of quadratic function What does the shape of the image of quadratic function have to do with? y=ax^2+bx+c
4. Induction: image and properties of quadratic function y = a (x + H) ² + k
5. Why is the vertex formula of quadratic function p (h, K)]: y = a (X-H) ^ 2 + k How did it come out?
6. Is there a better introduction to the image and properties of quadratic function y = a (X-H) 2K
7. The analytic expression of quadratic function is y = a (x + H) ^ 2 + K or y = a (X-H) ^ 2 + K
8. The larger the absolute value of the quadratic coefficient, the more open the parabola is?
9. 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?
10. Why the larger the value of | a | in quadratic function, the smaller the opening
11. 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?
12. What is the a value of quadratic function with the same image shape as function y = - x?
13. 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
14. 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|
15. 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
16. The quadratic function of higher one, the method to find the range of Y and the maximum value Y = x + √ 1-x, the value range of Y Y = x ^ 2 + √ 1-x ^ 2, find the value range of Y In y = 1 / √ ax ^ 2-ax + 1, X can take all real numbers and find the value range of A Let y = 4x ^ 2-4ax + A ^ 2-2a + 2, find the minimum value of y when x is less than or equal to 2 and greater than or equal to 0
17. Want to ask a high school mathematics about "the maximum value problem of quadratic function on closed interval" The problem is: find the maximum value of function y = x square - 2aX - 1 on [0,2] guys. I'm not good at math. I can't draw inferences from one instance~
18. The maximum value of quadratic function in closed interval Y = T ^ 2-2t + 3 - 1 / 4 ≤ t ≤ 2 find the maximum and minimum of Y
19. On the maximum value estimation of quadratic function on closed interval
20. A problem on the maximum value of closed interval of quadratic function I know that there are three possibilities, but when a ≤ 1 ≤ B, how can I judge whether to take a or B as the minimum? I see a solution (3) a