As shown in the figure, the minimum area of △ AOB can be obtained when the image of a function of degree passes through the point P (2,3), the positive half axis and a of the intersection x-axis, and the positive half axis and B of the intersection y-axis

Let y = KX + B, then 3 = 2K + B, then B = 3-2k, let y = 0, then x = - BK, then OA = - Bk. let x = 0, then y = B, then ob = B. s △ AOB = 12 × (- BK) × B = 12 × (3 − 2K) 2 − k = 12 × 4k2 − 12K + 9 − k = 12 [(2 − K-3 − K) 2 + 24] ≥ 12

RELATED INFORMATIONS

1. The image of the linear function y = x + 3 and the area of the triangle surrounded by the x-axis and y-axis are
2. The image of a given function passes through the intersection of the line y = - x + 1 and the X axis And the ordinate of the point of intersection with the Y axis is - 2, so we can find the analytic expression of this first-order function
3. It is known that the intersection of the image of y = (3a-7) x + A + 1 and the Y axis is above the X axis It is known that the intersection of the image of the first-order function y = (3a-7) x + A + 1 and the y-axis is above the x-axis, and when X1 is less than x2 The corresponding function value y satisfies that Y1 is greater than Y2, and the value range of a is obtained
4. For the first-order function y = (3a-7) x + A-2 of X, the intersection of the image and Y axis is below x, and Y decreases with the increase of X, then the value range of a is______ ．
5. It is known that the intersection point of the image and the Y-axis of the linear function y = (3a-7) x + A-2 of X is above the x-axis
6. Given that the image of a function passes through a point (1,2), and the product of the abscissa of the intersection of the image and the X axis and the ordinate of the intersection of the image and the Y axis is 9, the analytic expression of the function is obtained
7. Given that the image of the first-order function passes through a point (1,2), and the product of the abscissa of the intersection of the image and the x-axis and the ordinate of the y-axis is 9, the first-order function can be obtained
8. If the image of a function of degree passes through points (3,5) and (- 4, - 9), then the coordinates of the intersection of the image of the function and the y-axis are______ ．
9. If the image of a function of degree passes through points (3,5) and (- 4, - 9), then the coordinates of the intersection of the image of the function and the y-axis are______ ．
10. It is known that the intersection point of the image with the inverse scale function y = K / X and the linear function y = MX + n is a3,4 And the distance from the intersection of the image of the first-order function and the x-axis to the origin is 5 Finding two analytic expressions Find the coordinates of another point and determine what type of angle AOB is
11. It is known that the area of the triangle formed by the image of the linear function y = - 2x + B [b > 0] and two coordinate axes is equal to 9. Find the solution set of the value of B - 2x + B ≤ 0
12. If the image of positive scale function y = KX passes through the point (- 3,4), find the relation of this function
13. Given that the function value y of the positive scale function y = KX increases with the increase of X, the image of the first-order function y = K-X is approximately the same
14. Given that point a (x, - 4) and point B (3, y) are symmetric about X axis, then the value of X + y is___ ．
15. Given that point a (x, - 4) and point (3, y) are symmetric about X axis, then the value of X + y is
16. It is known that M = X-Y, n = XY, and m, n denotes (X & # 179; + Y & # 179;) &# 178; Such as the title
17. High school mathematics problem "please write the process" m = X-Y, n = XY, try to use the formula of M, n to express (x ^ 3 + y ^ 3) ^ 2
18. Given (x + y) ^ 2 = m, (X-Y) ^ 2 = n, try to use Mn to express (1) XY (2) x / y + Y / X
19. Given m = X-Y, n = XY, try m, n denotes (x ^ 2 + y ^ 2) ^ 2
20. Given m = x - y, n = XY, try to use M, n to represent (X3 + Y3) 2 The square of (the third power of X + the third power of Y)