As shown in the figure a (0,4) B (2,0), C is on the positive half axis of X axis, and the parabola y = AX2 + BX + C passes through ABC three points

(2) P5,71 / 4), q (13,55 / 4) or P (5,39 / 4), q (- 3,55 / 4) or P (5,21 / 4), q (3, - 5 / 4)

It is known that the parabola passes through two points a (1,0), B (0,3), and the axis of symmetry is a straight line x = 2

∵ the axis of symmetry of the parabola is a straight line x = 2 and passes through the point a (1,0). From the symmetry of the parabola, we can see that the parabola also passes through the point (3,0). Let the analytical formula of the parabola be y = a (x-x1) (x-x2) (a ≠ 0), that is, y = a (x-1) (x-3) and B (0,3) be substituted into: 3 = 3A ∵ a = 1 ∵ the analytical formula of the parabola is y = x2-4x + 3

RELATED INFORMATIONS

1. The axis of symmetry of the parabola y = ax ^ 2 + BX + C is x = 2, passing through (0,4) and (5,9) Write down the whole process
2. It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (find the analytic formula of the quadratic function, let the image intersect with the Y axis at point C, and find the area of △ ABC It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (1) to find the analytic formula of the quadratic function. (2) let the image intersect with the Y axis at point C, and find the area of △ ABC
3. The parabola y = AX2 + BX + C passes through point a (3,0). B (2, - 3) with x = 1 as the symmetry axis Is there a point P on the symmetry axis X = 1 so that PA = Pb in the triangle PAB? If so, find out the coordinates of point P. if not, explain the reason
4. Given that the vertex coordinates of a parabola are (- 2,1) and pass through points (1, - 2), the analytic formula of the parabola is obtained
5. If the parabola intersects the x-axis at points (2,0), (3,0) and the y-axis at points (0, - 4), then the expression of the quadratic function is________________ .
6. It is known that the parabola and X-axis intersect at two points a-1,0, b1,0, and the analytic expression of the function is obtained through m0,1
7. When the parabola y = ax square + BX + C passes through one, two and three image limits, then When the parabola y = ax square + BX + C passes through one, two, three image limits, then A.a>0,b>0,c=0 B.a>0,b
8. The maximum value of quadratic function y = ax & # 178; + BX + C is 4, and the image passes through the point (- 3,0)
9. Given that the quadratic function y = ax & # 178; + BX + C has the maximum value and is negative, then a =?. C =?
10. As shown in the figure, it is known that the image of quadratic function y = AX2 + BX + C (a, B, C are real numbers, a ≠ 0) passes through point C (T, 2) and intersects with X axis at two points a and B. if AC ⊥ BC, then the value of a is______ ．
11. Parabola y = 1 / 2x & # 178; + 1 can be regarded as parabola y = 1 / 2 (x + 3) &# 178; along X axis_ Translation_ Unit
12. When the parabola y = 2x-1 is translated upward by 2 units, the analytic expression of the function is_
13. Y = 1 / 2x + 1, y = 1 / 2x & # 178; - 3 / 2x + 1 find a point m on the symmetry axis of the parabola to make the value of ▏ am-mc ▏ maximum. (a is the intersection of the parabola and the Y axis, BC is the intersection of parabola and X axis, B is on the left side of C)
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