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) | Math enthusiast | Mathematical art

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)

(1) When x = - 1, the function has a maximum value of 2, let y = a (x + 1) &# - 178; + 2 substitute (- 2, - 1) into - 1 = a + 2, then a = - 3  y = - 3 (x + 1) &# - 178; + 2 (2) according to the fact that the symmetry axis is a straight line x = 1, we can know that another intersection point of the image on the X axis is: (3,0) let y = a (x + 1) (x-3) substitute (0, - 1) into - 1 = - 3a, then a = 1 / 3  y = 1 / 3 (x

RELATED INFORMATIONS

1. 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)
2. 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
3. What is the existence of quadratic function
4. 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?
5. 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?
6. Several analytic expressions of mathematical quadratic function What general form, vertex form and so on. Be clear
7. Finding the analytic expression of quadratic function （-1,0),(3,0),(1,-5) How can I get the analytic expression
8. A quadratic function knows how to find an expression for an image
9. 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
10. 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
11. 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
12. 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
13. 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____ .
14. 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
15. 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,
16. 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)
17. Explanation of quadratic function in senior one I don't know how to solve the problem
18. 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)
19. 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
20. 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?