Examples of reviewing and practicing quadratic function in ninth grade mathematics
1. (Dongcheng District, Beijing) has an image of a quadratic function. Three students described some characteristics of it: a: the symmetry axis is a straight line x = 4;; B: the abscissa of the two intersections with the X axis is an integer; C: The ordinate intersecting with the Y axis is also an integer, and the area of the triangle with these three intersections as its vertices is 3. Please write a quadratic resolution function that satisfies all the above characteristics. Test center: Comment on the solution of quadratic function Y = AX 2+BX+C: Let the analytical expression be y=a(x-x 1)(x-x2), let X .. The two intersections between the image and the X axis are A (X 1 0) and B (X2, 0), respectively. "Because the intersection point a(x-x 1)(x-x2) and the abscissa of the intersection point with the Y axis are 0, that is, the axis of symmetry of AX1x2: parabola is a straight line x=4, ∴x2-4=4-x 1, that is, X/. Available: x2=4+, x 1 = 4-∫x 1, x2 is an integer, ax 1x2 is also an integer, ∴ax 1x2 is a divisor of 3, and the acceptable value of * * is:/kloc. When AX 1x2 = 1, x2=7, x 1= 1, A = 1 when AX 1x2 = 3, x2=5, x1=. Then find out a from the conditions of the problem and see if c is an integer. If there is, the guess can be verified, just fill it in. 2. Psychologists in Anhui Province have found that there is a functional relationship between students' ability to accept concepts y and the time to put forward concepts x (unit: minutes): Y =-0. 1x2+2.6x+43 (0 ; At 13, y decreases with the increase of x, and the range of the independent variable of this function is: 0 < x3 < 0, so the two ranges should be 0 < x <13; 13