It is known that the symmetry axis of parabola y = AX2 + BX + C = - 1, intersects with X axis at two points a and B, intersects with y axis at C, where a (- 3,0), C (0,2) (1) Finding the function relation of parabola (2) Finding the coordinates of point B (3) There is always a point P on the symmetry axis, so that the perimeter of the triangle PBC is minimum, and the coordinates of point P are requested en

It is known that the symmetry axis of parabola y = AX2 + BX + C = - 1, intersects with X axis at two points a and B, intersects with y axis at C, where a (- 3,0), C (0,2) (1) Finding the function relation of parabola (2) Finding the coordinates of point B (3) There is always a point P on the symmetry axis, so that the perimeter of the triangle PBC is minimum, and the coordinates of point P are requested en

(1) The axis of symmetry is x = - 1, so - B / 2A = - 1 (1) point a is on the parabola 9a-3b + C = 0 (2) point C is on the parabola C = 2 (3) from (1), (2), (3), a = - 2 / 3, B = - 4 / 3, C = 2 the relation of parabola is y = - 2 / 3x ^ 2-4 / 3x + 2 (2) two points a and B are symmetric about x = - 1, so the coordinates of point B are (...)

It is known that the parabola y = - 1 / 2 (X-2) ^ 2 + 4 (1) the opening direction and the axis of symmetry of the parabola. (2) does the function y have a maximum or a minimum? And find out this function

Parabola y = - 1 / 2 (X-2) ^ 2 + 4
(1) The opening direction of the parabola is downward (because - 1 / 2)

The function y = (A2-1) X3 + (a + 1) x2 + X + (A-1) is a quadratic function. Find a and write the opening direction, axis of symmetry, vertex coordinates and X-axis intersection of the following parabola
（1）y=3x3+2x （2 y=-2x2+8x-8
Exercise 1: given that the two roots of the equation xsquare - 6x - 5 = 0 are x1x2, find the value of X1 square + x2 square
Tips:

The function y = (A2-1) X3 + (a + 1) x2 + X + (A-1) is quadratic,
therefore
a²-1=0
a+1≠0
therefore
a=1
y=2x²+x
（1）y=3x3+2x
There is something wrong with the title!
（2 y=-2x2+8x-8
The opening is downward; the axis of symmetry x = 2
Vertex (2,0)
The intersection of X axis is (2,0)
Exercise 1:
x1x2=-5
x1+x2=6
x1²+x2²=(x1+x2)²-2x1x2=36+10=46

For Y-axis symmetry and passing through points (1, - 2) and (- 2,0), the analytical expression of parabola is
Such as the title

Let the analytic formula of parabola be y = AX2 + BX + C, with respect to Y-axis symmetry, ∧ - B / (2a) = 0 --- > b = 0, and pass through points (1, - 2) and (- 2,0), and the following equations: - 2 = a + C, 4A + C = 0 are obtained: a = 2 / 3, C = - 8 / 3, ∧ the analytic formula of parabola is y = (2 / 3) x2-8 / 3