Type the coefficients of the quadratic equation and the solver will give you the roots, the y-intercept, the coordinates of the vertex and it will plot the function.

\[ \large a x^2 + b x + c = 0 \]**More About Critical Quadratic Equation**

The quadratic equation is an equation of the form:

\[a x^2 + b x + c = 0\]with \(a \ne 0\). It has solutions of the form

\[x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\]In order to analyze the nature of the solution, the discriminant is defined as:

\[D = b^2 – 4ac\]Based on the value of the discriminant, the nature of the solutions is defined. In fact, when \(D > 0\), then there are two different real solutions, when \(D = 0\), there is one repeated real solution, and when \(D < 0\), there are two different imaginary solutions.