![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
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
(1) if y = 1 / 2x ^ 2-x + C passes a (- 4,0), we can get: 0 = 8 + 4 + C, C = - 12, ｜ y = 1 / 2x ^ 2-x-12; (2) y = 1 / 2 (x ^ 2-2x + 1-1) - 12 = 1 / 2 (x-1) ^ 2-25 / 2, vertex m (1, - 25 / 2), let y = 0, that is, 1 / 2 (x-1) ^ 2-25 / 2 = 0, x = 6 or x = - 4, ｜ B (6,0), ab = 10 ｜ M '(1,25 / 2), mm' = 25, s tetragonal ambm '= 1 / 2
RELATED INFORMATIONS
- 1. 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)
- 2. 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)
- 3. 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)
- 4. Let f (x) = x ^ 2-2x + 2, let the minimum value of F (x) on [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 5. FX = x ^ 2-2x + 2, X ∈ [T, t + 1], t ∈ R, find the expression of the minimum value g (T) of function FX
- 6. 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)
- 7. 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)
- 8. The minimum value of the function f (x) = x2-4x-4 in the closed interval [T, t + 1] (t ∈ R) is denoted as G (T). (1) try to write the functional expression of G (T). (2) make the image of G (T) and find the minimum value of G (T)
- 9. F (x) = x2 + 4x + 3, t ∈ R, the function g (T) represents the minimum value of function f (x) in the interval [T, t + 1], and the expression of G (T) is obtained
- 10. Let the function FX = x + A / x + B (a > b > 0), find the monotone interval of F (x), and prove the increasing of F (x) in its monotone interval Sex
- 11. 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
- 12. 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
- 13. 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
- 14. 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
- 15. 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 °
- 16. 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
- 17. 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)
- 18. 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___ ．
- 19. The quadrant that the graph of a linear function y = - 5x + 3 does not pass through is______ ．
- 20. How many quadrants does the image of a linear function y = 5x + 2 pass through