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If the parabola y = ax & # 178; + K (a is not equal to 0) and y = - 2x & # 178; + 4 are symmetric about X axis, find the value of a, K
∵ y = ax & # 178; + K (a is not equal to 0) the equation of x-axis symmetry is y = - ax & # 178; - K
∵ y = ax & # 178; + K (a is not equal to 0) and y = - 2x & # 178; + 4 are symmetric about X axis
∴a＝2 k＝-4
The parabola y = (M-3) x square + (2m square - 7m + 3) x-3, the symmetry axis is Y axis, then M
The y-axis is x = 0
So x = - (2m & # 178; - 7m + 3) / [2 (M-3)] = 0
-(2m-1)(m-3)/[2(m-3)]=0
So 2m-1 = 0
m=1/2
It is known that the symmetry axis of parabola y = x square + (M + 2) + (2m-n) is a straight line x = - 3, and the vertex is on the x-axis. The values of M and N are obtained
From x = - 3, we can get: - 3 = - (M + 2) / 2
∴m=4.
The parabola can be reduced to y = x ^ 2 + 6x + 8-N = (x + 3) ^ 2 + 8-n-9 = (x + 3) ^ 2-1-n
From this, the vertex of the parabola is on the x-axis, we can get: - 1-N = 0
∴n=-1
To sum up, M = 4, n = - 1
If the ordinate of the lowest point of the parabola y = (m-1) x2 + 2mx + 2m-1 is zero, then M=______ ．
According to the meaning of the problem, according to the coordinate formula of the vertex of the function, 4ac-b24a = 4 (m-1) (2m-1) - (2m) 24 (m-1) = 0, the solution is m = 3 ± 52, and the parabola has the lowest point, the opening of the image is upward, ｜ M-1 ＞ 0, that is, m ＞ 1, ｜ M = 3 + 52
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