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