What's the relationship between x2-x1 in quadratic function Like x1x2 = A / C, X1 + x2 = - A / b

What's the relationship between x2-x1 in quadratic function Like x1x2 = A / C, X1 + x2 = - A / b

|X2-x1 | = radical ((x2 + x1) ^ 2-4x1x2)
=Radical ((B / a) ^ 2-4c / a)
=Radical ((b ^ 2-4ac) / A ^ 2)
=Root sign discriminant / | a|
I understand. Thank you!

How can I get the quadratic function y = a (x-x1) (x-x2)?
Please explain the process in detail, and. Be clean and clear, don't pile up, or you will be confused and can't understand

This form is called the zero form of quadratic function, which is also called two-point form. Suppose that the analytic form of quadratic function is y = ax & sup2; + BX + CX1, and X2 is two of the equations ax & sup2; + BX + C = 0. This shows that there must be (x-x1) and (x-x2) for factoring ax & sup2; + BX + C, and the product of these two factors if expanded

How to find a in the intersection of quadratic function y = a (x-x1) (x-x2)
How to get k after knowing the value of X1 and X2

For example: the parabola passes through points (1,0), (3,0) and (2,5) to find the analytical formula
Let the analytic formula be y = a (x-1) (x-3)
Substituting (2,5) into
5=a(2-1)(2-3)
So a = - 5
So the analytical formula of parabola is y = - 5 (x-1) (x-3)