General formula: y=ax^2 bx c(a, b, c are constants, a≠0)
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Top point formula: y=a(x-h)^2 k
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[vertex of a parabola P(h, k)]
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For the quadratic function y=ax^2 bx c
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Its vertex coordinates are (-b\/2a,(4ac-b^2)\/4a).
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derivation
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Y = ax 2 bx c y = a (x ^ 2 bx\/a c\/a) y = a (x ^ 2 bx\/a b ^ 2\/4A ^ 2 c\/a-B ^ 2\/4A ^ 2) y = a (x b \/ 2A) 2 c-B ^ 2\/4a y = a (x B \/ 2A) 2 (4AC-b ^ 2) \/ 4a
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The axis of symmetry x=-b\/2a
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Vertex coordinates (-b\/2a,(4ac-b^2)\/4a).
Formula: When the line is perpendicular to the X-axis, y=b, the midpoint of AA 'is on the line x=k, (a x) \/2=k, x=2k-a, so it is easy to find the coordinates of A' (2k-a, b), etc.