As shown in the figure, it is known that the quadrilateral ABCD is a parallelogram, BC = 2Ab, the coordinates of a and B are (1,0) (0,2) C respectively, and two points of D are on the graph of inverse scale function y = K / X The coordinate of point a is (10)

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• 1. Given that point a (1,3) is on the image of the function y = K (x > 0), the edge BC of rectangle ABCD is on the x-axis, and E is the midpoint of diagonal BD, The image of function y = K (x > 0) passes through two points a and E, and the abscissa of point E is m (1) Find the value of K (2) find the abscissa of point C (expressed by M) (3) when ∠ abd = 45 °, find the value of M It is required to have steps to solve the problem and clear thinking
• 2. It is known that point (1,3) is on the image of function y = KX (x > 0), the edge BC of rectangle ABCD is on the X axis, e is the midpoint of diagonal BD, the image of function y = KX (x > 0) passes through two points a and E, and the abscissa of point E is m. The following problems are solved: (1) find the value of K; (2) find the abscissa of point C; (3) find the value of m when ∠ abd = 45 °
• 3. It is known that: as shown in the figure, the edge BC of rectangle ABCD is on the x-axis, e is the intersection point of diagonal AC and BD, the image with inverse scale function y = 2x (x > 0) passes through two points a and E, and the ordinate of point E is m. (1) find out the coordinate of point a (expressed by M) (2) whether there is a real number m to make quadrilateral ABCD a square, if there is, ask for the value of M; if not, please explain the reason
• 4. Given that the image of function y = K-X (x > 0) passes through point (1,8), the edge BC of rectangle ABCD is on the x-axis Given that the image of function y = K (x > 0) passes through points (1,8), the edge BC of rectangle ABCD is on the X axis, e (m, n) is the midpoint of diagonal BD, and points a and E are on the image of function y = K (x > 0) 1. Use m to represent the abscissa of point C 2. Can rectangular ABCD be a square? If yes, find out the side length of the square; if not, explain the reason
• 5. It is known that the vertex of parabola y = (X-2) ^ 2-m ^ 2 (constant M greater than 0) is p Q: if the two intersections of the parabola and the x-axis are a and B from left to right, and the angle APB is 90 degrees, try to find the perimeter of the triangle APB
• 6. It is known that the vertex of parabola y = a (x-t-1) 2 + T2 (a, t are constants, a ≠ 0, t ≠ 0) is a, and the vertex of parabola y = x2-2x + 1 is B. (1) judge whether point a is on parabola y = x2-2x + 1, why? (2) If the parabola y = a (x-t-1) 2 + T2 passes through the point B, then ① find the value of a; ② can the two intersections of the parabola with the X axis and its vertex a form a right triangle? If you can, find out the value of T; if you can't, explain the reason
• 7. As shown in the figure, the image of the quadratic function y = 1 / 2x-x + C intersects with the X axis at two points a and B respectively. The symmetric point of vertex m about the X axis is m ' February 21, 2013 | sharing As shown in the figure, the image of the quadratic function y = 1 / 2x-x + C intersects with the X axis at two points a and B respectively. The symmetric point of vertex m about the X axis is m ' (1) If a (- 4,0), find the relation of quadratic function; (2) Under the condition of (1), calculate the area of the quadrilateral ambm '; (3) Is there a parabola y = 1 / 2x-x + C, so that the quadrilateral ambm 'is a square? If it exists, ask for the functional relation of the first parabola; if not, please explain the reason
• 8. Given that the minimum value of the function f (x) = x ^ 2-4x + 2 in the interval [T, T-2] is g (T), find the expression of G (T)
• 9. Let the minimum value of F (x) = x2-4x-4 on [T, t + 1] (t belongs to R) be g (T). Write out the functional expression of G (T)
• 10. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
• 11. As shown in the figure, it is known that the quadrilateral ABCD is a parallelogram, BC = 2Ab. The coordinates of two points a and B are (- 1,0), (0,2), respectively, and the coordinates of two points c and D are on the image of inverse scale function y = KX (k < 0), then K is equal to___ ．
• 12. The quadrant that the graph of a linear function y = - 5x + 3 does not pass through is______ ．
• 13. How many quadrants does the image of a linear function y = 5x + 2 pass through
• 14. How many quadrants does the image of linear function y = - 5x + 2 not pass through
• 15. 1. Translate the straight line y = 3x-2 upward by 4 units to get the straight line () 2. Which quadrant does the image of the first-order function y = 5x-2 pass through?
• 16. It is known that the image with the inverse scale function y = m / X passes through the point (- 2, - 3), and the image with the inverse scale function y = m / X is in the second and fourth quadrants, and the value of M is calculated
• 17. Given the inverse scale function y = (1 / 2 of m-2) x, the two branches of the image with the power of - 2 are in the second and fourth quadrant respectively, and the value of M is obtained
• 18. When n takes what value, the (n & # 178; + n-1) degree of y = (n & # 178; + 2n) x is an inverse scale function? In which quadrant is its image?
• 19. If the inverse scale function y = (k-1) x ^ k & # 178; - 5 passes through two or four quadrants, then k =?
• 20. Given that the image of a function y = 2mx + (6-3m & # 178;) passes through the origin and the second and fourth quadrants, then M=______