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The vertex coordinates of parabola y = x2-2x + 2 are______ ．
∵ y = x2-2x + 2 = (x-1) 2 + 1, the vertex coordinates are (1,1)
It is known that the vertex of parabola y = - x2 + 4x + Q is on the line y = 1 / 2x + 1
Finding the analytic expression of function
When x takes what value, y increases with the increase of X?
The vertex coordinates of parabola y = - X & # 178; + 4x + Q are [- B / (2a), (4ac-b & # 178;) / (4a)], where a = - 1, B = 4, C = Q
-b/(2a)=-4/(-2)=2
(4ac-b²)/(4a)=(-4q-16)/(-4)=q+4
So the vertex coordinates of the parabola are (2, q + 4)
Substituting x = 2, y = q + 4 into y = 1 / 2x + 1, we get the following result:
q+4=1/2×2+1
q+4=2
q=-2
Therefore, the analytical formula of parabola is y = - X & # 178; + 4x-2
y=-x²+4x-2
=-(x²-4x+4)+2
=-(x-2)²+2
The vertex coordinates of the parabola are (2,2), the opening is downward, and the axis of symmetry is x = 2
When x < 2, y increases with the increase of X
RELATED INFORMATIONS
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