If the image of parabola y = x2 + BX + 4 is shifted 3 units to the right and 2 units to the upper, the analytic expression of the image obtained is y = x2-2x + 3, then the value of B is () A. 2B. 4C. 6D. 8

If the image of parabola y = x2 + BX + 4 is shifted 3 units to the right and 2 units to the upper, the analytic expression of the image obtained is y = x2-2x + 3, then the value of B is () A. 2B. 4C. 6D. 8

∵ y = x2-2x + 3 = x2-2x + 1 + 2 = (x-1) 2 + 2, the vertex coordinates are (1,2), ∵ translate 3 units to the left, and then translate 2 units to the down, get (- 2,0), then the vertex coordinates of the original parabola y = x2 + BX + 4 are (- 2,0), ∵ the original parabola y = x2 + BX + 4 = (x + 2) 2 = x2 + 4x + 4, ∵ B = 4

By translating the parabola y = (x + 1) &# 178 downward by two unit lengths and then to the right by one unit length, the analytical formula of the parabola is____

Let the parabola y = (x + 1) &;
Down 2 unit lengths,
And then move it one unit length to the right,
The analytical expression of parabola obtained is
y=x²-2

The parabola y = 2x & # 178; + 3x + 5 / 2 is obtained by translating the parabola y = 2x & # 178; first to units and then to units

y=2(x²+3x/2)+5/2
=2(x²+3x/2+9/16-9/16)+5/2
=2(x²+3x/2+9/16)-9/8+5/2
=2(x+3/4)²+11/8
therefore
The parabola y = 2x & # 178; + 3x + 5 / 2 is obtained by translating the parabola y = 2x & # 178; 3 / 4 units to the left and 11 / 8 units to the up

The parabola F: y = x2-3x + 2 is translated one unit to the right, and then two units to the down to get the parabola f ′. 1. The analytic formula F ′ 2 is that the parabola f ′ intersects the x-axis
The parabola F: y = x2-3x + 2 is translated one unit to the right and then two units to the down to get the parabola f '
1. Analytical formula F ′
Let the parabola f ′ intersect the x-axis at a
B two points, intersect Y axis at C point, find a point D on the parabola below the straight line BC, make the area of △ BCD maximum, and find out the maximum area
3 under the condition of 2, make a straight line CG parallel to the x-axis through C, and intersect with the parabola f 'at point G, make a straight line DQ through point D, intersect AB at P, intersect CG at Q, and ask whether there is a point P on the line AB, so that the area of the trapezoid APQC is equal to the coordinate of 4 times the area of △ PBD? P

Answer: (1) the original parabolic equation is y = x ^ 2-3x + 2 = (x-3 / 2) ^ 2-1 / 4. According to the meaning of the title, we know that the moving parabola f 'is: (y + 2) = x ^ 2-3x + 2 = [(x-1) - 3 / 2] ^ 2-1 / 4, that is, f' is: y = (X-5 / 2) ^ 2-9 / 4 = x ^ 2-5x + 4 (2). According to the meaning of the title, the intersection a of the X axis of the parabola f 'should be on the left, B should be on the right: