Explanation of quadratic function in senior one I don't know how to solve the problem

Understand the connotation and essence of quadratic function. Quadratic function y = AX2 + BX + C (a ≠ 0, a, B, C are constants) contains two variables X, Y. as long as we first determine one of the variables, we can use the analytic formula to find another variable, that is, to get a group of

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1. Related analytic expressions of quadratic function The function f (x) satisfies the following conditions （1）f（1+x）=f（1-x） (2) The maximum value of F (x) is 15 (3) The sum of two cubes of F (x) = 0 equals 17 Find the analytic expression of F (x)
2. 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,
3. 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
4. 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____ .
5. 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
6. 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
7. 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)
8. 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)
9. 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
10. What is the existence of quadratic function
11. It is known that the domain of F (x) = (MX-1) √ (MX ^ - 4mx + 5) is the value range of R for M f(x)=(mx-1)/√（mx^-4mx+5)
12. A mathematical problem about "quadratic function" Are the two intersections of the image of the function y = x + (2k + 1) x + K and the X axis on the right side of the line x = 1? If so, please explain the reason; if not, request the value range of K when the two intersections are on the right side of the line x = 1
13. Two similar mathematical problems of quadratic function of one variable in junior high school In a football league, there are two matches between every two teams. There are 90 matches in total. How many pairs will take part in the match? 2. To organize a basketball league, the competition system is in the form of a single cycle (one game between each two teams), and 25 games are planned. How many teams should be invited to participate in the competition?
14. A Mathematical Olympiad problem of quadratic function of one variable It is known that the coordinates of a and B are (1,0), (2,0) respectively. If the image of quadratic function y = x ^ 2 + (A-3) x + 3 has an intersection with line AB, then the value range of a is?
15. Solving a mathematical quadratic function problem If it is known that the Square-1 of quadratic function y = 2x has the minimum value-1 in the interval [a, b], then the following relation must be true? A.0
16. The problem of quadratic function The relationship between the price and time t (unit: day) of a certain commodity in the supermarket in the recent 30 days is (T + 10) yuan, and the relationship between the sales volume and time t is (35-t), where t is greater than 0 and less than or equal to 30, and it is an integer. When does the commodity get the maximum daily sales amount? What is the maximum value?
17. A simple mathematical problem of quadratic function At the beginning, a businessman sold a certain commodity with a purchase price of 8 yuan per piece at 10 yuan per piece, and he could sell 100 pieces per day. He wanted to increase the price to increase the profit. Through the experiment, it was found that the daily sales of this commodity would decrease by 10 pieces per piece with a price increase of 1 yuan. Please write down the functional relationship between the price x (yuan / piece) and the daily profit y (yuan)
18. What is the intersection coordinate of parabola y = ax (square) and straight line y = a (square) x (square) (a is not equal to zero)?
19. On the ninth grade mathematical problems of quadratic function, a little difficult The quadratic function passes through points B (- 1,0) and C (3,0), its vertex is on the straight line y = kx-1, and the intersection Y axis of the quadratic function is on a 1) Find the axis of symmetry of the quadratic function 2) Finding the coordinates of point a (expressed by the algebraic expression of K) 3) Try to judge whether △ a 0b and △ AOC are similar, if all k values can be obtained It doesn't matter if you can work out a few questions~
20. Translate the parabola y = x ^ 2 + BX + C three unit lengths to the left, and then translate it two unit lengths to the upper, then get the parabola y = x ^ 2 + 3x + 6, and find the values of B and C