Quadratic function y = ax ^ 2 + BX + C The distance between the two intersection points of quadratic function y = ax ^ 2 + BX + C and X axis is 4 units. If the image is translated 1.5 units along the symmetric axis, then the image passes through the coordinate origin. If the original image is translated 2 units along the symmetric axis, then the image vertex is on the X axis, and the analytical formula of parabola is obtained

Quadratic function y = ax ^ 2 + BX + C The distance between the two intersection points of quadratic function y = ax ^ 2 + BX + C and X axis is 4 units. If the image is translated 1.5 units along the symmetric axis, then the image passes through the coordinate origin. If the original image is translated 2 units along the symmetric axis, then the image vertex is on the X axis, and the analytical formula of parabola is obtained

I don't know if y = 1 / 2x ^ 2 ± x-1.5 is right