Quadratic function (quadratic equation) discriminant calculator

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 quadratic equations (i.e., Vieta's theorem); the distribution of the roots of quadratic equations can be intuitively determined by using the graph of the quadratic function; the intersection of the graph of the quadratic function with the x-axis and the position of the graph can also be determined by the discriminant.

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

The discriminant is derived from this:

y=ax²+bx+c

The formula for the vertex is y=a(x+b/2a)²+(4ac-b²)/4a

Let's solve 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 one solution;

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