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As shown in the figure, the parabola y = 1 / 2x + MX + n (n ≠ 0) intersects the straight line y = x with two points AB, intersects the Y axis with points c, OA = ob, BC parallel to the X axis (1) The analytic formula of parabola (2) Let D and E be the two moving points on the line AB which are different from a and B (point E is above point d) de = root 2. Let D and E be parallel lines of Y axis, intersecting parabola and points F and g respectively. Let the abscissa of d be x and the area of quadrilateral degf be y. find the analytic expression of y about X, write out the value range of independent variable x, and find the maximum value of y when x is the value
1. BC ‖ X axis. X = 0, OC = - N - n = - 2n under the root sign, the solution is n = - 2
The analytical formula of parabola is y = 1 / 2x2 + X-2
2 (1) de = root 2, the abscissa of point D is x, (point E is above point d), so D (x, x) e (x + 1, x + 1), x + 1
If the intersection of the line y = - x-3 and the line y = 2x + 4 is in the first quadrant, then the value range of M is（
A．1＜m＜7
B．3＜m＜4
C．m＞1
D．m＜4
The straight line y = - x-3 moves m units upward, and the equation becomes y = - x-3 + M
The intersection with the line y = 2x + 4 is in the first quadrant,
2x+4=-x-3+m
3x=m-7
x＞0
m-7＞0
m＞7
There is no answer
If the title is a straight line y = - x + 3, then
2x+4=-x+3+m
3x=m-1
x＞0
m-1＞0
m＞1
The answer is C
(2013 · Tai'an) after the straight line y = - x + 3 is moved upward by M units, and the intersection point with the straight line y = 2x + 4 is in the first quadrant, then the value range of M is ()
A. 1＜m＜7B. 3＜m＜4C. m＞1D. m＜4
After the straight line y = - x + 3 moves m units upward, we can get: y = - x + 3 + m, the analytic formula of two straight lines is: y = - x + 3 + my = 2x + 4, the solution is: x = m − 13y = 2m + 103, that is, the intersection coordinate is (m − 13, 2m + 103), ∵ the intersection is in the first quadrant, ∵ m − 13 > 02m + 103 > 0, the solution is: M > 1
In the plane rectangular coordinate system, the line y = 2x + 1 is translated by 3 √ 2 ￣ units along the ray ocy = x direction, and the analytical expression of the translation line is obtained
First of all, the coordinate a of the intersection point of two straight lines is found to be (- 1, - 1) 3 √ 2 ￣ units along the ray ocy = x direction, which can be divided into two kinds: (1) 3 units of length are translated to the right, and 3 units of length are translated up at the same time. In this case, the coordinate of point a after translation is (2,2)
RELATED INFORMATIONS
- 1. In the plane rectangular coordinate system, a (1,3), B (2,1), OA ‖ BC, OC ‖ AB, try to use the knowledge of translation to find the coordinate of point C
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- 7. If it is known that a, B and C are not on the same line, then the parallelogram with the three points as the vertex has the same property
- 8. There are several parallelograms whose vertices are three points a, B and C which are not on a straight line A. 1 B.2 C.3 D.4
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- 10. Take three points a, B and C which are not on the same line as the three vertices to make parallelograms with different shapes. A total of () A. 1 B. 2 C. 3 d. 4
- 11. As shown in Figure 1, in the quadrilateral ABCD, AB is perpendicular to ad, CD is perpendicular to ad, and BC is rotated 90 ° counterclockwise around point B to get the line segment be, connecting AE and Ce (1) As shown in Figure 1, in the quadrilateral ABCD, AB is perpendicular to AD and CD is perpendicular to AD. rotate BC 90 ° counterclockwise around point B to get the line segment be and connect AE and Ce (1). If AB = 2cm and CD = 3cm, calculate the area of triangle Abe
- 12. In known trapezoid ABCD, AD / / BC, ∠ B = 90 degrees, ad = 3, BC = 5, ab = 1, rotate the line CD 90 degrees counterclockwise around point d to D and 90 degrees counterclockwise to de position What is the length of AE if AE is connected?
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