 # It is known that the image with parabola y = x square + BX + C translates 3 units to the right, and then translates 2 units downward to obtain the parabola Y = (x-3) square + 1, find the value of B and C

## It is known that the image with parabola y = x square + BX + C translates 3 units to the right, and then translates 2 units downward to obtain the parabola Y = (x-3) square + 1, find the value of B and C

b=0 c=3

### Parabola y = x2 + BX + C translates upward by 2 units, and then translates left by 4 units to obtain parabola y = X2, then the values of B and C are () respectively A. 6，4 B. -8，14 C. -6，6 D. -8，-14

Y = x2 translate 4 units to the right and then 2 units down to get y = (x-4) 2-2 = x2-8x + 14
So B = - 8, C = 14
Therefore: B

### First shift the square of parabola y = x + BX + C upward by 2 units, and then shift it left by 4 units to obtain the square of y = x and find the values of B and C Why can't you do it in the order of the questions? Yes - 8, - 18 But it was - 8,14

Parabola y = x ²+ The vertex coordinates of BX + C are [- B / 2, (4c-b) ²)/ 4] Parabola y = x ² The vertex coordinate of is (0,0) parabola y = X ²+ BX + C translates 2 units up and 4 units left to get y = X ² Translate 2 units upward, add 2 to the ordinate, and 4 units to the left, abscissa

### Translate the y = x square of the parabola to the right by 1 unit, and the functional expression of the parabola is

Shift 1 unit to the right and X becomes X - 1
So the function expression of parabola is y = (x - 1) ²

### Translate the general parabola formula to the right by 3 units and then down by 2 units. The analytical formula of the obtained image is the square of y = x minus 3x plus 5, then a + B + C =?

Y = x ^ 2-3x + 5 translates upward by 2 units, and then translates left by 3 units to obtain the original parabola Y1 = ax ^ 2 + BX + C
y1=(x+3)^2-3(x+3)+5+2=x^2+3x+7
a=1 b=3 c=7
a+b+c=11

### It is known that point a (- 2, - C) is translated 8 units to the right to obtain that both points a ', a and a' are on the parabola y = AX2 + BX + C, and the ordinate of the intersection of this parabola and Y axis is - 6, then the vertex coordinate of this parabola is () A. （2，-10） B. （2，-6） C. （4，-10） D. （4，-6）

From the ordinate of the intersection of parabola y = AX2 + BX + C and Y axis is - 6, C = - 6 is obtained,
‡ a (- 2,6), point a shifts 8 units to the right to obtain point a '(6,6),
∵ both a and a 'are on a parabola,

4a−2b−6＝6
36a+6b−6＝6 ， By solving this set of equations, we get
a＝1
b＝−4 ，
Therefore, the analytical formula of parabola is y = x2-4x-6 = (X-2) 2-10,
The coordinates of parabola vertex are (2, - 10)
So choose a