Quadratic Equations with one Variable

What do you mean by "quadratic equation?"   You probably have in mind something like

What restrictions do you place on the parameters a, b, and c?   We usually identify x as the variable and a, b, and  c are parameters from some domain.   For school mathematics the domain for the variable and the parameters is usually the set of real numbers but  a 0.

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In school mathematics we encounter "the" quadratic formula giving solution values for x.   

State that formula.   Is it the formula you see on the right?

 

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In some mathematics curricula, the formula is sometimes written in a slightly different way.  What is the point of that?   What interpretation might you give?

(Note that the first term on the RHS may be the midpoint of a segment.)

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Interpret 

The expression is called the discriminant of our quadratic equation.

Do a Google search for Discriminant of a Quadratic Equation.

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Use a Graphing program to illustrate and identify representations of the Quadratic function for a Quadratic Equation, its solution, the discriminant. and the midpoint for several examples.

You might also check out the Wikipedia images for the Discriminant of a quadratic equation with Google.