Current location - Training Enrollment Network - Mathematics courses - Handan Yimo 20 16 Mathematics
Handan Yimo 20 16 Mathematics
(1)∵ points c (-2,5) and d (0 0,3) are on the image of quadratic function y=x2+bx+c,

∴5=4? 2b+c? 3=c,

Solve b =? 2c=? 3.

(2) The analytical formula of parabola can be obtained from (1): y=x2-2x-3=(x- 1)2-4.

∴M( 1,-4),

When y=0, then x2-2x-3=0,

∴x 1=3,x2=- 1,

∴A(- 1,0),B(3,0),

∴AB=4,

∴S△ABM=4×42=8.

The coordinate of point P is (a, a2-2a-3). When the point p is above the x axis,

∴4(a2-2a-3)× 12=54×8,

Solution: a 1=4, a2=-2,

∴p(4.5) or (-2.5),

When the point p is lower than the x axis, the point does not exist.

P (4.5) or (-2.5).

(3) When the straight line y = x+m (m < 1) passes through the point D(0, -3),

∴-3=0+m,

∴m=-3;

When the straight line y=x+m has only one intersection with the parabola, x+m=x2-2x-3, that is, x2-3x-3-m=0,

δ= 9+4(3+m)= 0,

The solution is m=? 2 14.

To sum up, is the value of m 3 or? 2 14.