the quadratic equation ax²+bx+c=0 is a special case when the function value of the quadratic function y=ax²+bx+c is equal to zero. some quadratic function problems can be solved by using the relationship between the roots and coefficients of a quadratic equation (i.e. vedic theorem); the distribution of the roots of a quadratic equation can be intuitively determined using the image of the quadratic function; the image of the quadratic function the intersection point with the x-axis and the position of the image can also be judged using discriminants.

(4ac-b²)/4a is not a formula for judging the y-axis, it is the ordinate of the vertex in a general formula;

the discriminant is derived from this:

y=ax²+bx+c

the formula becomes the vertex formula as y=a(x+b/2a)²+(4ac-b²)/4a

let’s solve for y=0

y=0 means: a(x+b/2a)²+(4ac-b²)/4a=0

remove the denominator: 4a²(x+b/2a)²+(4ac-b²)=0

4a²(x+b/2a)²=b²-4ac

the left side of the equation is a non-negative number, obviously:

when b²-4ac<0, there is no solution;

when b²-4ac=0, there is a solution;

when b²-4ac>0, there are two solutions;