If the parabola y = ax + BX + C (a ≠ 0) passes through the origin, then Write relevant information

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• 1. The image of known parabola y = ax ^ 2 + BX + C passes through point a (1,0) B (4,6) (1) Find the analytical formula of the parabola (2) First, translate the parabola in (1) one unit to the left. How many translations up or down can make the parabola and the straight line AB have only one intersection? Write out the analytical formula of the parabola at this time (3) Translate the parabola in (2) 5 / 2 units to the right and t units to the down (T > 0). At this time, the parabola and X-axis intersect at two points m and N, and the line AB and y-axis intersect at point P. when t is the value, the area of the circle passing through M, N and P is the smallest? What is the minimum area? c=2
• 2. As shown in the figure, the parabola y = ax ^ 2 + 3 / 2x + C passes through the origin O and a (4,2), intersects the x-axis with point C, and the point m.n starts from the origin 0 at the same time, and the point m takes two single points The velocity of bit / s moves along the positive direction of y-axis, and point n moves along the positive direction of x-axis at the velocity of 1 unit / s. when one of the points stops moving, the other point stops (1). Find the analytical formula of parabola and the coordinates of point C; (2) in the process of point M. n moving, if the line Mn and OA intersect at point G, it is to judge the position relationship between Mn and OA, and explain the reason; Is there any time t that makes a quadrilateral with O, P, a and C as fixed points an isosceles trapezoid? If so, please explain the reason. {please hurry up,
• 3. It is known that the parabola y = x & # 178; + (2n-1) x + n & # 178; - 1 (n is a constant term) It is known that the parabola y = x & # 178; + (2n-1) x + n & # 178; - 1 (n is a constant term) (1) when the parabola passes through the origin and the vertex is in the fourth quadrant, the corresponding functional relationship is obtained. (2) Suppose that point a is a moving point on the parabola determined by (1), and it is located below the x-axis and on the left side of the symmetric state, passing through point a as a parallel line of the x-axis, intersecting the parabola with another point D, making ab ⊥ x-axis and point B, DC ⊥ X-axis at point C, then (1) when BC = 1, find the perimeter of rectangular ABCD (2) whether there is a maximum perimeter of rectangular ABCD? If it exists, calculate the maximum value and the coordinate of point A. if it does not exist, please explain the reason,
• 4. When a changes, the two tangent points are on the tangent line () respectively A:y=1/2 x²,y=3/2 x² B:y=3/2 x²,y=5/2 x² C:y=x²,y=3x² D:y=3x²,y=5x²
• 5. Translate the parabola y = x2 + 2x-8, make it pass through the origin, and write an analytical expression of the parabola after translation______ ．
• 6. Translate the parabola y = x2 + 2x-8, make it pass through the origin, and write an analytical expression of the parabola after translation______ ．
• 7. The translational parabola y = x ^ 2 + 2x + 8 is an analytical expression of the translational parabola written through the origin
• 8. Given the parabola y = x ^ 2-2x-8, translate the parabola along the X axis to make it pass through the origin? What does (1) translation along the X axis mean? (2) Does passing through the origin mean that the vertex of the parabola passes through the origin?
• 9. If the line y = kx-1 is translated upward by 3 units, and then to the right by 2 units, just passing through the origin, then K=
• 10. The parabola y = - (x + 3) ^ 2 shifts to the right by units just passing through the origin
• 11. If Tan α = 2, the abscissa of tangent P is 2, the distance from P to the origin can be obtained
• 12. Given the parabola y = x2 + 3x-5, find the tangent equation of the parabola at x = 3 Do with derivative
• 13. Parabola y = 3x & # 178; - X-2 the tangent equation of the intersection of parabola and x-axis is solved by means of Weida theorem
• 14. The tangent of a point P on the parabola y = x2-3x has an inclination angle of 45 degrees. It intersects with two coordinate axes at two points a and B. the AOB surface of the triangle can be obtained
• 15. Let p be any point on the parabola y = X3 - root 3x + 2 / 3, and the tangent slope at P is α, then the value range of angle α is obtained
• 16. The tangent equation of parabola y ^ 2 = x with slope 2 is
• 17. How to find the tangent slope of parabola x ^ 2 = 8 (y-b) at point (4, B + 2) RT
• 18. The known parabola y = x ^ 3, the slope of tangent at point x = 2 is?
• 19. The slope of the tangent at any point P (U, V) of the parabola y = x ^ 2 - 3x + 2 is calculated, and the equation of the tangent at the vertex of the parabola is obtained The answer I got is y = - 1 / 4
• 20. Given the parabola y = x & # 178; + 4 and the straight line y = x + 10, find: (1) the intersection of them; (2) the tangent equation of the parabola at the intersection. Solve it by derivative