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According to the following conditions, the expressions of the corresponding quadratic functions are obtained respectively 1. The image of known quadratic function passes through a (0, - 1) B (1,0) C (- 1,2) 2. It is known that the vertex of parabola is (1, - 3) and intersects with y axis at (0,1) 3. It is known that the parabola intersects the x-axis at (- 3,0) (5,0) and the y-axis at (0, - 3) 4. It is known that the vertex of the parabola is (3, - 2) and the distance between the two intersections of the parabola and the X axis is 4
(1) Let the expression of quadratic function be y = ax & # 178; + BX + C, and substitute it into three-point coordinates
c=-1,a+b+c=0,a-b+c=2.
The function expression is y = 2x & # 178; - X-1
(2) Let function expression be vertex form, y = a (x-1) &# 178; - 3, substitute (0,1)
a-3=1,a=4
The function expression is y = 4 (x-1) &# 178; - 3 = 4x & # 178; - 8x + 1
(3) Let the function expression be the intersection expression, y = a (x + 3) (X-5), substituting (0, - 3)
-15a=-3,a=1/5
The function expression is y = 1 / 5 (x + 3) (X-5) = x & # / 5-2x / 5-3
(4) Let the function expression be vertex form, y = a (x-3) &# - 2, because the symmetry axis of the function is x = 3, and the distance between the two intersection points and the symmetry axis is equal, so one of the intersection points is 2 units to the right of (3,0), which is (5,0)
Substitution point (5,0)
4a-2=0,a=1/2
The function expression is y = 1 / 2 (x-3) &# 178; - 2 = x & # 178; / 2-3x + 5 / 2
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