Why is the image of quadratic function a parabola

According to Niu Er's law, we can get that the trajectory of a parabola is a quadratic function!
Law content: the acceleration of an object is directly proportional to the combined external force F, inversely proportional to the mass of the object, and the direction of acceleration is the same as that of the combined external force,
Newton's second law of motion
In other words, the first derivative of momentum to time is equal to the sum of external forces

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1. The relation between quadratic function and parabola? What is the relationship between quadratic function and parabola
2. On the parabola of quadratic function For a parabola composed of three points a (- 1,0) B (3,0) C (0, - 1), the point q is on the Y-axis and the point P is on the parabola For a parabola composed of three points a (- 1,0) B (3,0) C (0, - 1), the point q is on the Y-axis and the point P is on the parabola. If we want to make the quadrilateral composed of point qpab a parallelogram, we need to find the coordinates of point P. sorry, we missed a parallelogram in the above problem
3. Why is a quadratic function a parabola The parabola is that the x-axis advances at constant speed VT, while the y-axis advances at ^ 2. How can we deduce that y is proportional to the square of X
4. Parabolic quadratic function problem It is known that the opening direction, shape and size of a parabola are the same as that of the parabola y = 3x * 2, and the vertex is on the vertex of the parabola y = (x + 2) * 2 Find the analytic formula of this parabola Let y = 3 (x + a) * 2 + B The vertex of parabola y = (x + 2) * 2 is (- 2,0) therefore y=3（x+2）*2 Why not set y = 3x * 2 + a
5. Quadratic function In y = (AX) 2 + BX + C, a determines the opening of parabola b. c.
6. It is known that the straight line y = - 2x + B, B is not equal to 0, intersects with X axis at point B; the analytic formula of a parabola is y = x square - [B + 10] x + C 1. If the parabola passes through point B and its vertex P is on the straight line y = - 2x + B, try to determine the analytical formula of the parabola; If the symmetric axis of the parabola just passes through point C, try to determine the analytical formula of the straight line y = - 2x + B!
7. Parabola of elementary third quadratic function It is known that there is a point C (0,2) d (4,6) on the x-axis in the plane Cartesian coordinates, and there is a point a whose distance from point C and point D is the smallest Finding the coordinates of point a
8. Practical problems of quadratic function Any one
9. A hotel room department has 60 rooms for tourists to live in. When the price of each room is 200 yuan per day, the room can be full. When the price of each room is increased by 10 yuan per day, there will be a room free. For a room with tourists, the hotel needs to pay 20 yuan per day for each room. Suppose the price of each room is increased by X yuan per day The functional relationship between the daily occupancy y (rooms) and X (yuan); (2) the functional relationship between the daily room charge P (yuan) and X (yuan); (3) the functional relationship between the daily profit w (yuan) and X (yuan) of the room department of the hotel; when the price of each room is how many yuan per day, w has the maximum value? What is the maximum value?
10. It is known that the circumference of the rectangle is 36cm, and the rectangle rotates around one of its sides to form a cylinder. When the length and width of the rectangle are respectively, the side area of rotation is the largest?
11. A.b.in the formula of parabola in quadratic function
12. The parabola image passes through a (0,1) B (1,2) C (2, - 1), and the analytic expression of quadratic function is obtained
13. 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?
14. Given the image of quadratic function as shown in the figure, find the relationship between 2A + B and 0
15. How to determine the sign of 2A + B (2a-b) in quadratic function?
16. What does the value of 2A + B in quadratic function image relate to
17. 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,
18. Why the larger the value of | a | in quadratic function, the smaller the opening
19. 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?
20. The larger the absolute value of the quadratic coefficient, the more open the parabola is?