How to get the intersection formula y = a (x-x1) (x-x2) of quadratic function

How to get the intersection formula y = a (x-x1) (x-x2) of quadratic function

Expand your formula y = a [x ^ 2 - (x1 + x2) x + x1x2], and the standard form of quadratic function is y = ax ^ 2 + BX + C, which can be converted to y = a (x ^ 2 + B / ax + C / a). In this case, the coefficients of quadratic terms - (Xi + x2) and + B / a refer to any number of X1 X2, so they express the same meaning. Similarly, x1x2 and C / a are the same, so both forms can be used As long as the expansion of formula has quadratic term, both the first term and the constant term are in the form of quadratic function

Given that the image of quadratic function passes through (- 1,10) (2,7) (1,4), the analytic expression of this function is obtained

Let the expression of the function be y = ax ^ 2 + BX + C
A set of equations is obtained by substituting the known three points into the expression
a-b+c=10
The joint solution of {4A + 2B + C = 7} gives a = 2, B = - 3, C = 5
a+b+c=4
Therefore, the number obtained from the above solution is substituted into:
The expression is y = 2x ^ 2-3x + 5