The vertex of the parabola y = ax's square + BX + C (a is not equal to 0) is m, and the focus of X axis is a and B (point B is on the right side of point a), △ ABM's three internal angles m and If the square of the quadratic equation (M-A) x with respect to x + 2bx + (M + a) = 0 has two equal real roots When the coordinates of vertex m are (- 2, - 1), find the analytical formula of the parabola and draw the general figure of the parabola;

The vertex of the parabola y = ax's square + BX + C (a is not equal to 0) is m, and the focus of X axis is a and B (point B is on the right side of point a), △ ABM's three internal angles m and If the square of the quadratic equation (M-A) x with respect to x + 2bx + (M + a) = 0 has two equal real roots When the coordinates of vertex m are (- 2, - 1), find the analytical formula of the parabola and draw the general figure of the parabola;

Because the vertex m is on the axis of symmetry, and the two points a and B are the intersection of the function image and the X axis, the ordinates are equal, so they are symmetrical about the axis of symmetry, so am = BM, that is, a = B quadratic equation has two equal real roots, so △ = (2b) & sup2; - 4 (M-A) (M + a) = 4B & sup2; - 4 (M & sup2; - A & sup2;) = 4B & sup2; + 4A & sup2

When θ changes, the vertex of parabola y & # 178; - 6ysin θ - 2x - 9cos & # 178; θ + 8cos, θ + 9 = 0 is on ellipse C, then the equation of ellipse C is

Parabola: Y & # 178; - 6ysin θ + 9sin & # 178; θ - 2x-9 (Sin & # 178; θ + cos & # 178; θ) + 8cos, θ + 9 = 0,
X=1/2(Y-3sinθ)^2+4cosθ,
Vertex coordinates: (4cos θ, 3sin θ),
X²/16+y²/9=1.

If the vertex is on the x-axis, the value of B is, if the vertex is on the y-axis, B =, if the parabola passes through the origin, B ==

1. The vertex is on the X axis
Δ=b²+4b-32=0
(b+8)(b-4)=0
B = - 8 or 4
2. The vertex is on the Y axis
b=0
3. Passing through the origin
0=8-b
b=8
If the explanation is not clear enough,

2 the image of this function y = ax + K passes through a [1,3] B [- 2, - 6] to find the analytic expression of this quadratic function

Substituting the two-point coordinates into the analytic formula: 3 = a + k - 6 = 4A + K, the solution is a = - 3, k = 6, so the analytic formula of the function is y = - 3x ^ 2 + 6