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
When the parabola y = - x ^ 2 + 2 (k-1) x + 2k-k ^ 2 passes through the origin, the analytic expression of the quadratic function is y = - x ^ 2-2x = (x + 1) ^ 2 + 1, intersecting with X axis a (0,0), B (- 2,0), and vertex C (- 1,1); △ ABC area = 1. K = 2, the analytic expression of the quadratic function is y = - x ^ 2 + 2x = (x-1) ^ 2 + 1, and X ·
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- 1. Find the solution of parabola y = 2x square - 4x + 5 about X axis, Y axis, origin, vertex symmetry
- 2. What is the length of the line segment cut by the square of the parabola y = x
- 3. What is the length of the line cut by the square of the parabola y = 2x + 5x-3 on the x-axis?
- 4. Square of parabola y = x, section line y = x, the length of line segment is
- 5. 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?
- 6. If the parabola y = (K + 1) x2 + k2-9 has a downward opening and passes through the origin, then K=______ .
- 7. As shown in Figure 11, parabola and straight line y = kx-4k (k)
- 8. 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
- 9. 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
- 10. Given the image of parabola C1: y = x ^ 2-2x as shown in the figure, fold the image of C1 along the Y axis to get the image of parabola C2 Given the image of parabola C1; y = x ^ 2-2x as shown in the figure, fold the image of C1 along the Y axis to get the image of parabola C2. 1) if the line y = x + B and parabola y = ax ^ 2 + BX + C (a is not equal to 0) have and only have one intersection, the line is said to be tangent to the parabola. If the line y = x + B is tangent to parabola C1, the value of B is calculated 2) When the line y = x + B and the image C1, C2 have two intersections, the value range of B
- 11. 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
- 12. 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
- 13. 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______ .
- 14. It is proved that the arcs added by two parallel strings of a circle are equal
- 15. 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?
- 16. The two arcs of the same string must be equal As above
- 17. How to prove that the arcs of two equal strings are equal
- 18. If the two strings of a circle are parallel to each other, are the arcs between the two strings equal?
- 19. 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
- 20. 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