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The axis of symmetry of the parabola y = (K & sup2; - 2) x & sup2; + m-4kx is a straight line x = 2, and its lowest point is in the straight line y = - 0.5x+ The axis of symmetry of parabola y = (K & sup2; - 2) x & sup2; + m-4kx is a straight line x = 2, and its lowest point is on the straight line y = - 0.5x + 2
From the symmetry axis X = 2, x = - B / 2A = 4K / 2 (k ^ 2-2) = 2,
k^2-k-2=0,
k1=-1,k2=2,
Because K ^ 2-2 is not 0, k = - 1
Substituting x = 2 into y = - 0.5x + 2, y = 1, vertex coordinates (2,1)
In the function, M = - 3
So: y = - x ^ 2 + 4x-3
It is known that the axis of symmetry of the parabola y = 5x + BX + C is x = - 2, and the minimum value is 7. Find the analytic expression of the function and the values of B and C
Y = 5x ^ 2 + BX + C = 5 (x ^ 2 + BX / 5) + C = 5 (x ^ 2 + BX / 5 + B ^ 2 / 100) + C - B ^ 2 / 20 = 5 (x + B / 10) ^ 2 + C-B ^ 2 / 20 because the axis of symmetry is x = - 2, so x = - B / 10 = - 2b = 20, because the minimum value is 7, then C-B ^ 2 / 20 = C-20 = 7C = 27, so the analytical formula is y = 5x ^ 2 + 20x + 27
If the axis of symmetry of a parabola is x = 1 and has a unique common point with X axis, and the opening direction is downward, then the analytical formula of the parabola is______ Write any one
Let the quadratic function y = AX2 + BX + C, the ∵ axis of symmetry be x = 1 and have a unique common point with X axis, and the opening direction is downward, ∵ a < 0, B = - 2A, △ = 0, that is, b2-4ac = 0. For example, y = - x2 + 2x-1
RELATED INFORMATIONS
- 1. If the image of parabola y = x2 + BX + 4 is shifted 3 units to the right and 2 units to the upper, the analytic expression of the image obtained is y = x2-2x + 3, then the value of B is () A. 2B. 4C. 6D. 8
- 2. In the plane rectangular coordinate system, translate the parabola to the right y = x + 6x + 8 to make it pass through the origin, and write an analytical formula of the parabola after translation!
- 3. As shown in the figure, in the plane rectangular coordinate system xoy, it is known that the symmetry axis of the parabola is the Y axis, passing through (0,1), (- 4,5) two points 1 find the expression of the parabola 2. Given the coordinates (0,2) of point F, let the abscissa of any point P on the parabola be x0, make PM perpendicular to the x-axis at point m, connect PF, express the line segment PM and line segment PF with the formula containing x0, and compare the size of PM and PF 3 let the straight line PQ passing through point F intersect the parabola at another point Q. try to judge the position relationship between the circle with diameter PQ and the x-axis and explain the reason
- 4. In the plane rectangular coordinate system, it is known that the parabola passes through two points a (- 4.0) and B (0. - 4), and the axis of symmetry is a straight line x = - 1 If the point m is a point on the parabola in the third quadrant, the abscissa of the point m is m, and the area of the triangle mAb is s, the function of s with respect to m is obtained. If the point P is a moving point on the parabola and the point q is a moving point on the straight line y = - x, judge that there are several positions that can make the quadrilateral with the point pqbo as the vertex be a parallelogram, and write the corresponding point Q coordinates
- 5. It is known that the parabola y = (- 1 / 7) x ^ 2 + BX + C and the positive half axis of X axis intersect at two points a and B, ab = 4, P is a point on the parabola, and its abscissa is 9, Angle PbO = 135 degrees, cot angle PAB = 7 / 3 (1) Finding the coordinates of point P (2) finding the relation of parabola It's a problem about quadratic function
- 6. On the solution of sine function area Know: y = sin (3x - п / 2) = a (0 < a > 1) find: sum of all real number roots in the interval [0,2 Π]
- 7. How to find the length of sine function How to find the curve length of y = 0.184sin π X in a period
- 8. Y = cosx, X belongs to [0,3 π / 2], find the area enclosed by the curve and the coordinate axis
- 9. Find the monotone interval of function y = 3sin (2x + π / 4) y = 1 + SiNx y = - cosx is not a number of sine cosine, regardless of the numbers and signs in front of it I want to know why
- 10. A formula for the area of a triangle bounded by a linear function and a coordinate axis, Well, it's very complicated. I can't understand it
- 11. After the parabola y = - X2 is shifted 2 units to the left, the analytical expression of the parabola is () A. y=-（x+2）2B. y=-x2+2C. y=-（x-2）2D. y=-x2-2
- 12. The parabola y = x & # 178; + BX + C is obtained by moving the parabola y = x & # 178; + BX + C upward by 2 units and then to the left by 1 unit
- 13. The area of the figure enclosed by y = ex, x = 0 and y = e is______ ．
- 14. The following is an expanded view of a cuboid carton (1) How much iron sheet does it need to make this iron box? (2) What is the volume of this iron box in milliliter Unit centimeter
- 15. Find the area of SiNx enclosed by [0,2 π] and x-axis
- 16. Let p be a point on the curve C: y = - 1 / 3x & # 179; + X & # 178; - 2x + A, and the inclination angle a of the tangent line of curve C at point P, then the value range of a is obtained (2) given the function f (x) = ㏑ x, G (x) = ax & # 178; / 2 + 2x (a ≠ 0), if f ′ (x) > G ′ is constant on (0, + ∞), the value range of a is obtained
- 17. In the plane rectangular coordinate system, given a (x, y), and xy = - 2, try to write two points that satisfy the condition
- 18. If (X-Y) 2 + M = x2 + XY + Y2, then the value of M is () A. xyB. 0C. 2xyD. 3xy
- 19. Point P (x, y) is a point in the plane rectangular coordinate system. If XY > 0, then point P is in; if xy = 0, then point P is in; if the square of X + the square of y = 0, then point P is in
- 20. It is known that in the plane rectangular coordinate system, the coordinate of point a is (4,0), point B is any point on the positive half axis of Y axis, AC = 2, and point C is in the first quadrant, then tan The value range of ∠ BOC is ()