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As shown in the figure, in diamond shaped ABCO, the coordinates of point B are (3,3), and the coordinates of point C are () A. （0，2）B. （0，3）C. （0，2）D. （0，3）
In RT △ CDB, BD = 3, OD = 3, let CD = x, then BC = OC = 3-x, then (3) 2 + x2 = (3-x) 2, and the solution is x = 1.. OC = od-cd = 2
Do all quadratic function images pass through the origin
The topic is in the plane instruction coordinate system, The image of the first-order function y = ax + B and the second-order function y = ax + BX + CDE may be a (the second-order function crosses the origin and intersects the first-order function on the X axis), B (the second-order function crosses the origin and intersects the first-order function on the X axis), C (the second-order function crosses the origin but does not intersect the first-order function), D (the second-order function crosses the origin but does not intersect the first-order function), and the last correct option is a, I want to ask the quadratic function is not necessarily over the origin, why a is correct
Because the explanation of the answer is that the quadratic function should pass through the origin first, excluding B, the quadratic function must intersect with the primary function at x, excluding D, so choose a, many of the quadratic functions I have learned do not need to pass through the origin, why the correct answer he gave is not that the quadratic function passing through the origin is correct, but it is wrong
You don't see the meaning of the question clearly! The meaning of the question is to ask you which of the following may be correct! Not absolutely correct! Just discuss the possible situation of these two images! For example, option B, when the quadratic function and the primary function intersect on the X axis, then you can exit. The quadratic function must cross the origin! In other words, "if the quadratic function is not the origin, So it's impossible to intersect with the first-order function and the x-axis (but there is an intersection point), so B is wrong! Similarly, C and D are also wrong. Here we give a simple proof of B. (we hope you can think about other items). Suppose that the first-order function intersects with the x-axis, then the intersection point is (- B / A, 0) because this is the common intersection point of the first-order function and the second-order function, then bring this point into the second-order function to get: a (B / a) ^ 2-B (B / a) + C = 0. The first two terms just disappear and get C = 0. So this means that the second-order function passes through (0,0) point. Do you understand!
The image of quadratic function y = 1 / 4 x square is a parabola. What is its focal coordinate
y=x^2/4
That is, x ^ 2 = 4Y = 2PY, P = 2
The opening is upward, and the focus is on the Y axis. The focus coordinate is (O, P / 2), that is, the focus coordinate is (0,1)
If we know that the square of quadratic function y = x plus [K + 2] x plus K has two different focal points on the sub half axis of X axis, we can get the range of value of K
That is to say, the equation x ^ 2 + (K + 2) x + k = 0 has two different negative roots
There are two different roots
So the discriminant = k ^ 2 + 4K + 4-4k > 0
K ^ 2 + 4 > 0
x1+x2=-(k+2),x1*x2=k
x10
So k > 0
RELATED INFORMATIONS
- 1. The image of quadratic function y = 1 / 16 of the square is a parabola, and its focal coordinate is
- 2. As shown in the figure, the quadrilateral oabc is a right angled trapezoid. It is known that ab ∥ OC, BC ⊥ OC, the coordinates of point a are (3,4), ab = 6. (1) find out the analytic function of the straight line OA; (2) find out the perimeter of the trapezoid oabc; (3) if the moving point P moves along the direction of O ﹥ a ﹥ B ﹥ C (excluding O and C), and the distance of point P is s, write out the coordinates of point p; (expressed by the algebraic formula containing s) (4) if the straight line L passes through point d (3,0), and the line L divides the perimeter of right angle trapezoid oabc into two parts: 5:7
- 3. As shown in the figure, it is known that there is a straight line and a curve in the rectangular coordinate system. This straight line, X axis and Y axis intersect at point a and point B respectively, and OA = ob = 1 This curve is a branch of the image of the function y = 2x / 1 in the first quadrant. Point P is any point on this curve, and its coordinates are (a, b). The perpendicular lines PM and PN made from point P to X and Y axes, and the perpendicular feet are m and n. the straight line AB intersects PM and PN at points E and f respectively. (1) it is proved that AF # 8226; be = 1 (2) the coordinates of points E and F are obtained respectively (the coordinates of point e are represented by the algebraic expression of a, and the coordinates of point e are expressed by the algebraic expression of A, Using the algebraic expression of B to express the coordinates of point F, we only need to write the results, not the calculation process); (3) Calculate the area of △ OEF (the result is expressed by the algebraic formula containing a and b); (4) Please prove whether △ AOF and △ BOE are necessarily similar; if not, briefly explain the reasons (5) When the point P moves on the curve y = 2x / 1, △ OEF changes accordingly. Point out the size of the angle whose size remains unchanged among the three internal angles of △ OEF, and prove your conclusion
- 4. Let the equation of the line L1 be x + 2y-2 = 0, and rotate the line L1 90 ° counterclockwise around the origin to get the line L2, then the equation of L2 is______ ．
- 5. The straight line M: x-2y = 0 rotates 45 degrees counterclockwise around the point P (2,1) to obtain the straight line L, and the equation of the straight line L is obtained
- 6. If the line X-Y + (3 ^ - 1) - 1 = 0 is rotated 15 degrees counterclockwise around points (1, 3 ^ - 1), the equation of the line L is?
- 7. In the plane Cartesian coordinate system, when the point a (4,2) is rotated 90 ° counterclockwise around the origin, the coordinate of the corresponding point a 'is____
- 8. Rotate the triangle 90 ° anticlockwise around point a for the first time, the second time and the third time respectively Rotate the triangle 90 ° anticlockwise around point a each time to draw the first, second and third rotation figures respectively. Use C1, C2 and C3 to represent the position of point C after rotation, and use number pairs to represent it. Connect C, C1, C2, C3 and C in turn to see what the figure is. Speed up
- 9. Draw a triangle AOB and rotate 90 ° counterclockwise around o point
- 10. Take a point p outside a right triangle ABC and rotate it 180 degrees counter clockwise. How to draw?
- 11. The coordinates of points a, B and C are (3,0), (1, 3 under the root sign) and (0,1) respectively (4 / 4) the coordinates of points a, B and C are (3,0), (1, 3 under the root sign) and (0,1) respectively to find the area of the quadrilateral oabc
- 12. As shown in the figure, the vertices a, D and C of oabc and ADEF are on the coordinate axis, the point F is on the line AB, and the points B and E are on the function As shown in the figure, the vertices a, D and C of oabc and ADEF are on the coordinate axis, the point F is on the line AB, and the points B and E are on the function y = 1 / X (x)
- 13. If 1 + Tana / 1-taba = 3 + 2 √ 2, then sin2a How to simplify Cosa √ 2siina
- 14. Given x2 + y2 = 1, find the maximum and minimum of 2x + y Maximum value related to circle
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- 16. Factorization factor: x2-2xy + y2-4=______ ．
- 17. [2/xy/(1/x+1/y)2+(x2+y2)/(x2+2xy+y2)]*2x/(x-y)
- 18. Given that C is the half focal length of the ellipse x2a2 + y2b2 = 1 (a > b > 0), then the value range of B + Ca is______ ．
- 19. 1/2xy+y2+1+x2-1/2xy-2xy-1
- 20. If the eccentricities passing through hyperbola x2 / a2-y2 / B2 = 1 and ellipse x2 / M2 + Y2 / B2 = 1 (a > 0, M > b > 0) are reciprocal to each other, then the triangle with a, B.M as side length What triangle is it? Can it be an isosceles right triangle?