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)

f(x) = x^2 - 4x - 4 = (x - 2)^2 - 8
It can be seen that f (x) has a minimum value of - 8 when x = 2, a decreasing function when x < 2, and an increasing function when x > 2
So:
one

RELATED INFORMATIONS

1. 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)
2. 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)
3. FX = x ^ 2-2x + 2, X ∈ [T, t + 1], t ∈ R, find the expression of the minimum value g (T) of function FX
4. 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)
5. 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)
6. 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)
7. 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
8. 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
9. Draw the graph of function f (x) = | x ^ 2 + X-2 | and write the monotone interval
10. What is the relationship between derivative function and monotonicity of function? What is the relationship between derivative function and monotonicity of function? How to draw function image by derivative function, or draw derivative function by function? Please give specific examples. Is there a better way to remember them?
11. 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)
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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 °
18. 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
19. 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)
20. 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___ ．