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It is known that the parabola y = AX2 + BX + C (a ≠ 0) passes through the point a (1,0), the equation of symmetry axis is x = 3, the vertex B, the line y = KX + m passes through two points a and B, and the area of the triangle enclosed by it and the coordinate axis is 2. The analytic solutions of the first-order function y = KX + m and the second-order function y = ax & # 178; + BX + C are obtained
Let B (3, n), then n = 3K + M ①
If a straight line passes a, then 0 = K + M ②
And | m | - M / K | - 2 = 2 ③
From ①, ② and ③, we can get: k = 4 M = - 4 N = 8, or: k = - 4 M = 4 N = - 8
Let the parabolic equation be y = a (x-3) &# 178; + 8, or y = a (x-3) &# 178; - 8
The solution of generation point (1,0) is a = - 2 and 2
Ψ y = - 2 (x-3) & # 178; + 8, or y = 2 (x-3) & # 178; - 8
That is: y = - 2x & # 178; = 12x-10, or y = 2x & # 178; - 12x + 10
If the symmetry axis of the parabola y = ax ^ 2 + BX + C is a straight line x = 2 and the minimum value is 2, then the root of the equation AX ^ 2 + BX + C = 2 about X is
The symmetry axis of parabola y = ax ^ 2 + BX + C is a straight line x = 2, and the minimum value is 2,
The vertex of parabola is (2,2)
That is, x = 2, y = ax ^ 2 + BX + C = 2
The equation AX ^ 2 + BX + C = 2 of X is the minimum value of the function, then it passes through the lowest point
So when ax ^ 2 + BX + C = 2, x = 2
If the intersection coordinates of the parabola y = AX2 + BX + C and the X axis are (- 3,0) and (- 1,0), then the equation of the axis of symmetry of the parabola is______
The intersection coordinates of parabola y = AX2 + BX + C and X axis are (- 3,0) and (- 1,0),
Then - 3 and - 1 are the two roots of AX2 + BX + C = 0
From the Veda theorem, we know (- 3) + (- 1) = - B / A
That is - B / a = - 4
So - B / 2A = - 2
The symmetry axis of y = AX2 + BX + C is x = - B / 2A
So the equation of symmetry axis of parabola is x = - 2
RELATED INFORMATIONS
- 1. If the axis of symmetry of the parabola y = AX2 + BX + C (a ≠ 0) is a straight line x = 2 and the minimum value is - 2, then the root of the equation AX2 + BX + C = - 2 about X is______ ．
- 2. Given the curve y = 1 / 3x3 + 4 / 3, find the tangent equation of the curve passing through the point P (2,4) The tangent point is not P Suppose the tangent point Q (a, a & # 179 / / 3 + 4 / 3) Slope f '(a) = A & # 178; y-(a³/3+4/3)=a²(x-a) Over P 4-a³/3-4/3=a²(2-a) a³-3a²+4=0 (a+1)(a-2)²=0 A = 2 is p So here a = - 1, so x-y-2 = 0 Where the slope f '(a) = A & # 178; how does it come from?
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- 8. If (X-Y) 2 + M = x2 + XY + Y2, then the value of M is () A. xyB. 0C. 2xyD. 3xy
- 9. In the plane rectangular coordinate system, given a (x, y), and xy = - 2, try to write two points that satisfy the condition
- 10. Let p be a point on the curve C: y = - 1 / 3x & # 179; + X & # 178; - 2x + A, and the inclination angle a of the tangent line of curve C at point P, then the value range of a is obtained (2) given the function f (x) = ㏑ x, G (x) = ax & # 178; / 2 + 2x (a ≠ 0), if f ′ (x) > G ′ is constant on (0, + ∞), the value range of a is obtained
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