Introduction to Quadratic Equations

Fireworks accompany festive celebrations around the world. (Credit: modification of work by tlc, Flickr)

The trajectories of fireworks are modeled by quadratic equations. The equations can be used to predict the maximum height of a firework and the number of seconds it will take from launch to explosion. In this tutorial, we will study the properties of quadratic equations, solve them, graph them, and see how they are applied as models of various situations.

Solving Quadratic Equations Using the Square Root Property

Quadratic equations are equations of the form \(a{x}^{2}+bx+c=0\), where \(a\ne 0\). They differ from linear equations by including a term with the variable raised to the second power. We use different methods to solve quadratic equations than linear equations, because just adding, subtracting, multiplying, and dividing terms will not isolate the variable.

We have seen that some quadratic equations can be solved by factoring. In this tutorial, we will use three other methods to solve quadratic equations.