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If the parabola y = 2 (x + 3) (x + m) intersects with the x-axis and two points a and B (a is on the left side of B) and OA: OB = 3:1, find the value of M
According to the parabolic equation, the coordinates of the two intersections are (- 3,0) (- m, 0)
∵OA:OB=3:1 OA=3
∴OB=1
The coordinates of point B are (- 1,0) or (1,0)
∴m=±1
The parabola y = AX2 + 2aX + C and X-axis intersect at two points a and B, a left and b right, and ab = 4 to find the coordinates of a and B
The symmetry axis of the image is x = - 2A / (2a) = - 1
So the midpoint of AB is (- 1,0)
Since AB = 4, the abscissa of a is - 1-2 = - 3, so a (- 3,0)
The abscissa of B is - 1 + 2 = 1, so B (1,0)
Given that the point a (- 2,6) is on the parabola y = x & # 178; + BX + C, and the ordinate of the intersection of the parabola and the Y axis is - 6, find the vertex of the parabola
Substituting the points (- 2,6) and (0, - 6) into the parabola, we get the following results:
(-2)²-2b+c=6 ①
c=-6 ②
The solution is: B = - 4, C = - 6
∴ y=x²-4x+6
The axis of symmetry x = - B / 2A = - (- 4) / 2 = 2
(4ac-b²)/4a=(-24-16)/4=-10
The vertex coordinates are (2, - 10)
It is known that the intersection of the parabola y = AX2 + BX + C and the x-axis is a (- 1,0), B (3,0), the intersection of the parabola y = AX2 + BX + C and the y-axis is point C, and the vertex is point D,
If the area of the quadrilateral ABCD is 18, find the analytical formula of the parabola
I have the correct answer is y = 2x2-4x-6 or y = - 2x2-4x-6
According to the meaning of the title, if a parabola is open up or down, and x = 1 is its axis, then - B / 2A = 1,
And a and B have two equations on the parabola
According to the fact that the area of a quadrilateral is equal to the area of each triangle, there is another equation,
A, B, C can be solved simultaneously
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