Quadratic equation

A quadratic equation is an equation where its highest exponent is 2 (which is why it is called 'quadratic' from the Latin word quadratus 'square'). These equations can be rearranged to the standard form which is^[1]ː

${\displaystyle ax^{2}+bx+c=0\,,}$

where a is not equal to 0, otherwise the equation is linear.

It makes a parabola (a "U" shape) when graphed on a coordinate plane. When people work with quadratic equations, one of the most common things they do is to solve it. This means to find the points on a coordinate grid where the graphed equation crosses the x-axis, or the horizontal axis. These points are called the "zeroes", or "roots", of a function. In other words, to solve the equation means to find the value of x so that ${\displaystyle ax^{2}+bx+c=0}$, where the coefficients, a, b, and c, are all real numbers. There are different ways to find out the value of x. Plotting the function on a graph is one way. In the picture on the right, the function crosses the x-axis at the points ${\displaystyle (-1,0)}$ and ${\displaystyle (2,0)}$.

Graphing a quadratic equation makes it is very easy to find the roots, but it is not always convenient. So there are different ways to do this using math.

1. ↑ Charles P. McKeague (2014). Intermediate Algebra with Trigonometry (reprinted ed.). Academic Press. p. 219. ISBN 978-1-4832-1875-5. Extract of page 219