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As shown in the figure, in the plane rectangular coordinate system, the image of quadratic function intersects C at Y axis, a and B at x axis, points a and B are on both sides of the origin The coordinate of a is (- 3,0), Ao = co = 3BO (1) Find this quadratic function expression (2) If the point d (- 2, y) is a point on the parabola, find the area of △ BCD (3) In (2), if point P is a moving point between B and D on the parabola, when P moves to what position, the area of △ BDP is the largest? Find the coordinates of point P and the maximum area of △ BDP!
(1) Let y = ax ^ 2 + bx-3, let the intersection point of the parabola and X axis be C and B, then the two are - 3 and 1 - 3 + 1 = - B / a (- 3) * 1 = (- 3) / A, so a = 1, B = 2, so the function formula is y = x ^ 2 + 2x-3 (2) d (- 2, y). By substituting the function formula, the area of y = - 3 triangle BDP = 1 / 2 * (1 - (- 3)) * | - 3 | 6 (3)
In the plane rectangular coordinate system, the image of the quadratic function y = x2-bx-c intersects with the X axis at two points a and B, a is on the left side of the origin, B (3,0), and intersects C with the Y axis（ Point 0, - 3), P is a moving point on the parabola below the line BC (1) Find the expression of this quadratic function (2) Connect Po and PC, and fold the triangle POC along CO to get quadrilateral pop 'C. is there a point P so that the quadrilateral pop' C is diamond? If so, ask for the coordinates of point P at this time. If not, please explain the reason, (3) When the point P moves to what position, the area of the quadrilateral ABPC is the largest, and the coordinates of the point P and the maximum area of the quadrilateral open ABPC are calculated
1. The analytic formula of quadratic function can be obtained as follows: y = x? - 2x-3; 2, set the coordinates of point P (x, y), when the quadrilateral pop 'C is a diamond, ∵ Po = PC, PP' ⊥ OC, OC = 3, ? YP = - 3 / 2, when YP = - 3 / 2, - 3 / 2 = x? - 2x-3, we can get: x = ± √ 10 / 2 + 1, ? x > 0, ? x = 1 + √ 10 / 2, ? 10 / 2
As shown in the figure, it is known that the two diagonals of the parallelogram ABCD intersect the origin of the plane rectangular coordinate system. If the coordinates of point a are (- 2,3), then the coordinates of point C are______ .
∵ in the parallelogram ABCD, point a and point C are symmetric about the origin,
The coordinates of point C are (2, - 3)
So the answer is: (2, - 3)
In the plane rectangular coordinate system, O is known as the origin, in the plane rectangular coordinate system, O is known as the origin, and the quadrilateral ABCD is a rectangle, A. The coordinates of B and C are a (- 3,1) B (- 3,3) C (2,3) d (2,1) (2) Move the rectangle ABCD horizontally to the right at the speed of 1 unit length per second. After 2 seconds, the coordinates of the quadrilateral A1, B1, C1 and D1 are respectively? (3) In translation (2), the area of the rectangle a1b1c1d1 after a few seconds = the area of the rectangle ABCD? The answer to the third question is 3.5 seconds. Please set it after T seconds
(2) A1(-1,1)B1(-1,3)C1(4,3)D1(4,1)
(3) Let T seconds later be equal to the area of the rectangle
At this time, B1 abscissa is - 1 + T, D1 abscissa is 4 + t,
In this way, the area of the quadrilateral omc1n can be calculated, which is 3x (4 + T)
The area of triangle od1n is 0.5x (4 + T), the area of triangle omb1 is 0.5x3x (- 1 + T), and the area of triangle b1c1d1 is 5
Subtract the area of three triangles from the area of quadrilateral omc1n, which is 10
That is: 3 (4 + T) - 0.5 (4 + T) - 0.5x3x (- 1 + T) - 5 = 10
T = 3.5
As shown in the figure, in quadrilateral ABCD, O is the origin of plane rectangular coordinate system, the coordinates of points a and C are (3,0), (0,5), and point B is in the first quadrant (1) Write the coordinates of point B [no answer] (2) If the straight line CD passing through point C intersects AB with point D, and the circumference of the rectangular oabc is divided into two parts of 1:3, the coordinates of point D are obtained (3) If the line CD in (2) is shifted down by 2 units, the resulting line is c ` d '. Try to calculate the area of the quadrilateral oad ` C'
(2) if point D is on the straight line AB, the coordinates of point d (3, y) may be set
According to the meaning of the title, 0 ＜ y ＜ 5
∵ CD divides the circumference of rectangular oabc into 1:3 parts
∴(CB+BD):(OC+OA+AD)=1:3
That is (3 + 5-y): (3 + 5 + y) = 1:3
The solution is y = 4
So the coordinates of point d (3,4)
(3) if the line CD in (2) is shifted downward by 2 units, then c '(0,3), d' (3,2)
Then ad '= 2, OC' = 3, OA = 3
It can be seen from the figure that the quad oad ` C 'is a right angled trapezoid
The area of the quad oad ` C '= (ad' + OC ') OA / 2
=(2+3)×3÷2
=7.5
In the plane rectangular coordinate system, the diagonal intersection o of the parallelogram ABCD is the origin, and the coordinates of the two vertices a and B are a (1,2) B (- 3,1) Coordinates of the other two points c and D of the parallelogram ABCD (urgent!)
C（-1,-2）D（-1,3）
In this paper, we use the coordinate of a + N + N + 5 to construct the coordinate of the same point in the plane
Because n + 1
As shown in the figure, the vertex a (2,4) and B (1,2) C (5,3) of the parallelogram ABCD in the plane rectangular coordinate system
The corresponding point D is (6,5), and the coordinates of the center of gravity are the coordinates of the diagonal intersection point. The intersection point is on the midpoint of AC, and the intersection point is also their midpoint. If the intersection is e, then the x-axis of point E is half of (2 + 5), and point E is half of (4 + 3) on the y-axis
In the plane rectangular coordinate system, the coordinates of vertices a, B and C of the parallelogram ABCD are (0,0) (3,0) (4,2), then the coordinates of vertex D are a. (7,2) B. (5,8) C. (1,2) d. (2,1) why a is wrong
Although (7,2) and the three points in question can form a parallelogram, is it because the problem has already stated that it is a parallelogram ABCD? If you select item a, the order of the four vertices should be abdc, right~
As shown in the figure, in the plane rectangular coordinate system, the point P (x, y) is the point on the line y = - x + 6 in the first quadrant, the point a (5,0) O is the coordinate origin, and the area of triangle Pao is s (1) Find the function analytic formula between S and X (2) Write the value range of the independent variable x and draw the image of function s (3) Xiao Ming thinks that the area of triangle OPA can be 5,15,20. What do you think?
1.S=1/2*5y=5/2(-x+6)
Two
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