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

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• 1. 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
• 2. It is known that the parabola y = 2x2 + 4x + k-1 has two intersections with the x-axis
• 3. It is known that the parabola y = (k-1) x2 + 2kx + K-2 has two different intersections with the X axis (1) (2) when k is an integer and the solution of the equation 3x = kx-1 about X is negative, find the analytical formula of the parabola; (3) under the condition of (2), if you draw the largest square in the closed graph surrounded by the parabola and X axis, so that one side of the square is on the X axis and the two ends of the opposite side are on the parabola, try to find the largest square What's your side length?
• 4. Parabola y = 2x ^ 2 + 1 and parabola y = - 2x ^ 2 + k are at most the same_____ Intersection points
• 5. Translate the square of the parabola y = 2x left and right so that it intersects the X axis at point a and the Y axis at point B. if the area of △ AOB is 8, find the analytical formula of the parabola after translation
• 6. Find the standard equation of a parabola satisfying the following conditions. On the parabola y ^ 2 = 24ax (a > 0), there is a point m whose abscissa is 3 and its distance from the focus is 5
• 7. In a parabola, the distance from the focus to the collimator is 4, and the focus is on the y-axis. Write out the standard equation of the parabola and find the solution
• 8. Write the standard equation of parabola according to the following conditions: (1) the focal point is f (0,3), (2) the distance from the focal point to the collimator is 2
• 9. Given that the vertex is at the origin and the focus is on the Y-axis of the parabola C section line y = 2x-1, the chord length is 2 root sign 10, and the equation of parabola C is obtained
• 10. Through the focus F of parabola y2 = 4ax (a > 0), make two mutually perpendicular focus chords AB and CD, and find the minimum value of | ab | + | CD |
• 11. The coordinates of the intersection of the parabola 2x ^ 2-3x-5 and the X axis are
• 12. Using image to find the coordinates of the intersection of the square + 3x + 5 of parabola y = - 2x and X axis
• 13. Is there an intersection between the parabola y = x2-2x-3 and y = x + 1? If so, find the coordinates of the intersection
• 14. Find the intersection coordinates of parabola y = x2 + 1 and straight line y = 2x + 9
• 15. The intersection coordinates of the line y = 2x + 2 and the parabola y = x2 + 3x are______ ．
• 16. The coordinates of the intersection of the line y = x + 2 and the parabola y = x2 + 2x are______ ，______ ．
• 17. 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
• 18. 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?
• 19. 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
• 20. 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