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In the plane rectangular coordinate system, the intersection of the parabola Y1 = x ^ 2-2x + A and the X axis is a, and the intersection of the parabola y2 = x ^ 2 + 2x + 1 + 2a and the X axis is B, and B is symmetric about the Y axis, a is a real number (1) Calculate the value of a and the coordinates of a and B; (2) Do the parabola Y1 and Y2 intersect at a point C on the y-axis? If they intersect at the same point, ask for the area of the largest triangle ABC. If they do not intersect at the same point, please explain the reason
And when y = 0, we're going to be able to do all of the following: 1-A, and as y = 0, we're going to be able to (x-1) & sup2; (X-1-1) & sup2; (x-1) & sup2; (X-1-1) & sup2; (X-1-1) & sup2; (X-1-1) & sup2; (X-1-1) & sup2; (and (1-A) - 1 (1-A), when y = 0, when y = 0, when y = 0, we're going to be able, and when y = 0, we're going to be able, and when y = 0, we're going to be able, we're going to be able, when we're going to be able, we are going to be able, we, and we are going to be able, we are going to be able, we are going to be able, and we are going to be able, when we are going to be able, and when we are going to be able, the results show that: 1-A = 1-2a, a = 0, Y1 and Y2 all cross the origin, We have only the first question for x 1 = 2, x 2 = - 2, a (2,0), B (- 2,0)
RELATED INFORMATIONS
- 1. Given that the points a (a, Y1), B (2a, Y2), C (3a, Y3) are all on the parabola y = 1 / 2x ^ 2-1 / 2x, find the intersection of the parabola and X-axis? How to find the area of triangle ABC when a = 1? 3. Is there any equation which contains Y1, Y2, Y3 and has nothing to do with a? If so, try to give one and prove it: if not, explain the reason?
- 2. Given that the points a (a, Y1), B (2a, Y2), C (3a, Y3) are on the parabola y = 5x * x + 12x, find the coordinates of the intersection of the parabola and the X axis (2) When a = 1, find the area of △ ABC
- 3. The coordinates of the intersection of the line y = x + 2 and the parabola y = x2 + 2x are______ ，______ ．
- 4. The intersection coordinates of the line y = 2x + 2 and the parabola y = x2 + 3x are______ ．
- 5. Find the intersection coordinates of parabola y = x2 + 1 and straight line y = 2x + 9
- 6. Is there an intersection between the parabola y = x2-2x-3 and y = x + 1? If so, find the coordinates of the intersection
- 7. Using image to find the coordinates of the intersection of the square + 3x + 5 of parabola y = - 2x and X axis
- 8. The coordinates of the intersection of the parabola 2x ^ 2-3x-5 and the X axis are
- 9. It is known that the parabola y = x2 square-2x-8. The two intersections of the parabola and the X axis are a and B respectively (a is on the left side of B), and its vertex is p. find the surface of the triangle ABP
- 10. If the parabola y = (1-k) x ^ 2-2x-1 has two intersections with the X axis, then the value range of K is the same RT
- 11. In the plane rectangular coordinate system, the line L and the parabola y ^ 2 = 2x intersect at two points a and B (1) Prove: "if the line L passes through the point t (3,0), then the product of vector OA and vector ob = 3" is a true proposition (2) Write down the inverse proposition of the proposition in (1), judge the truth and explain the reason
- 12. The parabola y = - 1 / 2x square + 3 / 2x + 2 intersects the X axis at two points a and B, and intersects the Y axis at point C (1) ABC is a right triangle (2) : the straight line x = m (0 ∠ m ∠ 4) moves on the line ob, intersects the x-axis at point D, intersects the parabola at point E, intersects BC at point F. when m = what, EF = DF? (3) : after connecting CE and be, "is there a point e to maximize the area of triangle BCE?" if there is a point E, calculate the coordinates of point E and the maximum area of triangle BCE
- 13. As shown in the figure, in the plane rectangular coordinate system xoy, the analytical expression of the parabola is
- 14. If the quadratic functions f 1 (x) and F 2 (x) satisfy the following conditions: (1) f (x) = f 1 (x) + F 2 (x) monotonically decreases on R; (2) g (x) = f 1 (x) - F 2 (x) pairs (2) For any real number x1, X2 (x1 ≠ x2), if G (x1) + G (x2) / 2 > G (x1 + x2 / 2), then F1 (x) = F2 (x)=
- 15. If the quadratic function F1 (x) - a1x ^ 2 + b1x + C1, F2 (x) = a2x ^ 2 + b2x + C2, such that F1 (x) + F2 (x) is an increasing function on R, please give the following result If the quadratic function F1 (x) - a1x ^ 2 + b1x + C1, F2 (x) = a2x ^ 2 + b2x + C2, such that F1 (x) + F2 (x) is an increasing function on R, please give a set of F1 (x) =? F2 =?
- 16. If the quadratic functions F1 (x) = a1x ^ 2 + b1x + C1 and F2 (x) = a2x ^ 2 + b2x + C2 such that F2 (x) + F1 (x) is listed as an increasing function in (- ∞, + ∞), the condition is
- 17. If the quadratic functions F1 (x) = a1x2 + b1x + C1 and F2 (x) = a2x2 + b2x + C2, let F1 (x) + F2 (x) be an increasing function on (- ∞, + ∞) if______ ．
- 18. 1. Given the function Y1 = x (x > 0) and function y2 = 1 / X (x > 0), then=____ The minimum value of Y1 + Y2 is____ . 2. Given function Y1 = x + 1 (x > - 1) and function y2 = (x + 1) & # + 4 (x > - 1), then=____ The minimum value of Y2 / Y1 is___ .
- 19. Given the function y = y1-y2, where Y1 and X are in positive proportion, Y2 and X are in inverse proportion, and when x = 1, y = 1; when x = 3, y = 5
- 20. If we know that the two tangents of parabola C1: y2 = x + 1 and parabola C2: y2 = - x-a are perpendicular at the intersection, we can find a