It is known that the image of the function y = KX + m intersects with the opening downward parabola y = ax & # 178; + BX + C at two points a (0,1) B (- 1,0) (1) Find the analytic expression of the function y = KX + M (2) If there is an intersection C between the parabola and the x-axis, and the length of the line AC is the root 5, the analytic expression of the quadratic function y = ax & # 178; + BX + C is obtained

(1) the image of ∵ function y = KX + m is solved by a (0,1) B (- 1,0) two points ∵ M = 1, - K + M = 0 to get k = 1, M = 1 ∵ the first-order function is y = x + 1 ∵ OA = | 1 | 1, CA = √ 5, ∠ AOC = 90 °, OC = √ (AC & # 178; - OA & # 178;) = √ [(√ 5) &# 178; - 1 & # 178;] = 2, that is, the abscissa of C is 2 or

The vertex of parabola y = 2 (X-2) square-7 is C, and the image of function y = - kx-3 passes through C, then k =?

The vertex is (2, - 7)
-7=-2k-3
k=2

RELATED INFORMATIONS

1. If y = ax & # 178; + BX + C and X-axis intersection (- 2,0) (1,0), its shape and opening direction are the same as the parabola y = - X & # 178;, then the parabola analytical formula
2. The intersection of the parabola Yax & # 178; + BX + C (a > 0) and the x-axis is a (x1,0), B (x2,0). The solution set of X10 is the inequality ax & # 178; + BX + C < 0?
3. If we know that the image of a function y = ax + B passes through a point (2,1), then the description of parabola y = ax ^ 2-bx + 3 is correct If the image of a function y = ax + B passes through a point (2,1), then the parabola y = ax ^ 2-bx + 3 is described as follows: (1) passing through a fixed point (- 2,5); (2) the axis of symmetry can be x = 1; (3) passing through a fixed point (0,3), (4) when a > 0, the maximum value of the ordinate of the vertex is 3; (5) when a < 0, the minimum value of the ordinate of the vertex is 3, (6) It is possible that B = - 2A_________________ .）
4. If the image of a function y = ax + B passes through (- 2,1), then the image of a parabola y = ax2-bx + 3 passes through () A. （-2，1）B. （2，1）C. （2，-1）D. （-2，-1）
5. Let the distance between the parabola y = x ^ 2 + ax + A-2 and the two intersections of X axis be 2, then the value of a is?
6. The shortest distance from parabola x ^ 2 = y to straight line 2x-y-4 = 0 is? The answer is (3 root 5) / 5,
7. Find a point P on the parabola y2 = 4x, so that the distance between the point P and the line y = x + 3 is the shortest
8. If the sum of the distance from a point P to a (3, - 1) on the parabola y ^ 2 = x and the distance to the focus f is the smallest, what is the coordinate of point P
9. If the focus of the parabola X & # 178; = 2PY (P > 0) coincides with the upper focus of the ellipse X & # 178 / / 3 + Y & # 178 / / 4 = 1, 1) solve the parabolic equation 2) if AB is For the moving chord passing through the focus of the parabola, the straight lines L1 and L2 are the two tangent lines of the parabola tangent to a and B respectively, and the ordinates of the focus of L1 and L2 are calculated
10. Given the parabola y & #178; = 2x, set point a (a, 0) (a > 0), find the coordinates of point P nearest to point a on the parabola and the corresponding distance | PA |
11. Given that the image of the function y = (K squared-k) x squared + KX + (K + 1) is a parabola, is the value range of K ≠ 1
12. The focus of parabola y = - x square + K and X axis is a (a, 0), B (B, 0). If a square + b square = 4, find the value of K
13. Given that the parabola y = X2 - (k-1) x-3k-2 intersects the X axis at two points a (α, 0), B (β, 0), and α 2 + β 2 = 17, the value of K is obtained
14. Given the parabola y = x square - (k-1) x-3k-2 and the x-axis image is called two points a (a, 0), B (B, 0), and a square + b square = 17, find K
15. As shown in the figure, it is known that the line y = KX + B intersects the parabola y = x2 ^ with P and Q, the abscissa of P is 2 and intersects the X axis with m (2,0) to find the expression of the line y = KX + B Find the area of the triangle formed by the point P, Q and the origin The abscissa of P is - 2
16. The image of quadratic function y = ax ^ 2 + C passes through points a (1, - 3), B (- 2, - 6) Find this first-order function
17. The vertex of the parabola y = ax's square + BX + C (a is not equal to 0) is m, and the focus of X axis is a and B (point B is on the right side of point a), △ ABM's three internal angles m and If the square of the quadratic equation (M-A) x with respect to x + 2bx + (M + a) = 0 has two equal real roots When the coordinates of vertex m are (- 2, - 1), find the analytical formula of the parabola and draw the general figure of the parabola;
18. As shown in the figure, it is known that the image of quadratic function y = AX2 + BX + C (a, B, C are real numbers, a ≠ 0) passes through point C (T, 2) and intersects with X axis at two points a and B. if AC ⊥ BC, then the value of a is______ ．
19. Given that the quadratic function y = ax & # 178; + BX + C has the maximum value and is negative, then a =?. C =?
20. The maximum value of quadratic function y = ax & # 178; + BX + C is 4, and the image passes through the point (- 3,0)