It is known that the two different intersections of the parabola y = AX2 + 2x + C and X-axis are on the right side of the origin, then the point m (a, c) is on the second side___ &Quadrant

When a ＞ 0, △ 4-4ac ＞ 0f (0) = C ＞ 0-22a ＞ 0, there is no solution; when a ＜ 0, △ 4-4ac ＞ 0f (0) = C ＜ 0-22a ＞ 0, then a ＜ 0, C ＜ 0; then point (a, c) is in the third quadrant

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1. If the parabola y = - x ^ 2 + 2 (k-1) x + 2k-k ^ 2 passes through the origin and opens downward, find: 1 the analytic expression of quadratic function 2. The area of triangle formed by intersection A.B and vertex C of X axis
2. Find the solution of parabola y = 2x square - 4x + 5 about X axis, Y axis, origin, vertex symmetry
3. What is the length of the line segment cut by the square of the parabola y = x
4. What is the length of the line cut by the square of the parabola y = 2x + 5x-3 on the x-axis?
5. Square of parabola y = x, section line y = x, the length of line segment is
6. It is known that there are two different points e (K + 3, - K2 + 1) and f (- k-1, - K2 + 1) on the parabola y = - x2 + BX + 4 It is known that there are two different points e (K + 3, - K2 + 1) and f (- k-1, - K2 + 1) on the parabola y = - x2 + BX + 4 (1) Find the analytical formula of parabola; (2) As shown in the figure, the parabola y = - X & # 178; + BX + 4 intersects with the positive half axis of X axis and Y axis at points a and B respectively, M is the midpoint of AB, PMQ rotates with m as the center on the same side of AB, and PMQ = 45 °, MP intersects with y axis at point C, MQ intersects with X axis at point D; (3) Under the condition of (2), when the values of M and N are, the edge of ∠ PMQ passes through the point F?
7. If the parabola y = (K + 1) x2 + k2-9 has a downward opening and passes through the origin, then K=______ ．
8. As shown in Figure 11, parabola and straight line y = kx-4k (k)
9. Given the curve y = - x ^ 3 + 2x, find the linear equation which passes through point B (2,0) and is tangent to curve C? Derivative = -= I set a point (x0, Y0), and then f (x0 + △ x) - f (x0) / △ x, want to find its derivative function = = but it's so strange, is it - △ x ^ 2-3x0 ^ 2-3 △ xX0 + 1, is it my method problem or wrong calculation? = = because I feel that △ x should all be reduced
10. The curve C1: y = x ^ 2yu and C2: y = - (X-2) ^ 2, the line L and C1C2 are tangent, find the equation of the line L. use the derivative function of two curves to find out why it can't be used
11. Given the parabola y = 2 (K + 1) x2 + 4kx + 2k-3, when we find out the value of K, the two intersections of the parabola and X axis are located on both sides of the origin? Answer x1x2
12. If the parabola y = 2x2-4x-5 is translated 3 units to the left and 2 units to the upper, the parabola C is obtained, then the analytical formula of parabola c about Y-axis symmetry is______ ．
13. It is proved that the arcs added by two parallel strings of a circle are equal
14. In the same circle or equal circle, the arcs and chords opposite by equal circle angles are not equal There is another question: why is the degree of the arc equal to that of the central angle? Is the degree of an arc equal to that of a circle?
15. The two arcs of the same string must be equal As above
16. How to prove that the arcs of two equal strings are equal
17. If the two strings of a circle are parallel to each other, are the arcs between the two strings equal?
18. As shown in the figure, the parabola y = - X & # 178; + 2 (k-1) x + K + 1 intersects the X axis at two points a and B, and intersects the Y axis at point C. the length ratio of line OA to ob is 1:3 (1) Finding the analytic formula of parabola and the coordinates of two points a and B (2) The circle d with diameter AB intersects with the positive half axis of Y axis at point e. the tangent line of circle D is made through e, and the X axis intersects with point F. the coordinates of point F are calculated AB is on the opposite side of Y axis
19. A straight line with a slope of 1 intersects with a parabola y2 = 2x at two different points a and B. find the trajectory equation of the midpoint m of the line ab
20. It is known that the square of a straight line passing through point P (2,0) with a slope of 4 / 3 and a parabola y = 2x intersect at two points a and B. let the midpoint of line AB be M. Find the coordinates of point M. how to teach the students this problem, The answer seems to be m (41 / 16,3 / 4). How can I tell the students?