Algebra Tutorials

The Quadratic Equation Formula: The meaning of the term -b/2a

You have probably wondered many times what is the meaning of the quadratic formula. I mean, you probably know how to use the formula, this is, if you are presented with a problem involving some kind of quadratic equation, you know that the following formula needs to be used:

x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}

For example, if you are asked to solve the equation: $2x^2 -10x + 12 = 0$ , then you know it is a quadratic equation, and in this case, $a = 2$ , $b = -10$ and $c = 12$ . So then we have to plug those values into the quadratic equation formula:

x = \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \frac{-(-10) \pm \sqrt{(10)^2-4(2)(12)} }{2(2)}

= \frac{10 \pm \sqrt{100-96} }{4} = \frac{10 \pm \sqrt{4} }{4} = \frac{10 \pm 2}{4}

which means that the solutions are $x_1 = 2$ and $x_2 = 3$ .

But what is the meaning of the term -b/2a in the quadratic formula?? It is very useful to have the proper intuition about it.

The term -b/2a has a clear graphical interpretation, and it corresponds to the position of the symmetry axis that is defined by the graph of the quadratic formula. So then, simply, the term -b/2a is the "center" of the parabola defined by a quadratic equation.

You can see a video below with a good tutorial on how to use the quadratic equation in various different contexts.