It is known that the parabola y = 2x2 + 4x + k-1 has two intersections with the x-axis

According to the meaning of the title, △ = 16-8 (k-1) > 0, ∧ K < 3

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1. 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?
2. Parabola y = 2x ^ 2 + 1 and parabola y = - 2x ^ 2 + k are at most the same_____ Intersection points
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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 |
9. Make a straight line with a slope of 45 degrees through the focus f with the square of parabola y = 4x, intersect the parabola at two points a and B, and find the distance from the midpoint C of AB to the parabola collimator
10. Given the parabola y & sup2; = 4x, make a straight line with an inclination angle of π / 4 through its focus F, intersect the parabola at two points a and B, let the vertex of the parabola be o, and find △ a Given the parabola y & # 178; = 4x, make a straight line through its focus f with an inclination angle of π / 4, intersect the parabola at two points a and B, let the vertex of the parabola be o, and calculate the area of △ ABC
11. 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
12. 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
13. The coordinates of the intersection of the parabola 2x ^ 2-3x-5 and the X axis are
14. Using image to find the coordinates of the intersection of the square + 3x + 5 of parabola y = - 2x and X axis
15. Is there an intersection between the parabola y = x2-2x-3 and y = x + 1? If so, find the coordinates of the intersection
16. Find the intersection coordinates of parabola y = x2 + 1 and straight line y = 2x + 9
17. The intersection coordinates of the line y = 2x + 2 and the parabola y = x2 + 3x are______ ．
18. The coordinates of the intersection of the line y = x + 2 and the parabola y = x2 + 2x are______ ，______ ．
19. 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
20. 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?