Solving Quadratic Equations by Graphing

Solving Quadratic Equations by Graphing

Author: chris ludbrook

1.  Estimate soutions of quadratic equations by graphing or examining data.

2.  Find solutions of quadratic equations using various methods of factoring.

3.  Find solutions of quadratic equations using the quadratic formula.



A quadratic equation is formed with a quadratic function is set equal to a value.  When a quadratic equation is written in the form  where a ≠ 0, it is said to be in standard form.  The solutions to a quadratic equation are also known as roots.

There are various methods that we can use to solve quadratic equations.  We can estimate the roots by graphing the equation or examining the data.  You should remember that graphing is not a prefered method as it is difficult to determine exact values due to the inaccuracy that is intrinsic in graphing.  To find exact roots, we will use several factoring techniques and the quadratic equation.



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Solving Quadratics by Graphing

Graphing is a crude means to finding exact roots, but it can be used for estimating values. As you become proficient at graphing quadratics by hand, you may find quicker ways to estimate these values such as websites, software, or a graphing calculator.

Solving Quadratics by Examining Data

Graphing gives a pretty strong estimate of the x-intercepts, or solutions, of a quadratic equation. Here's another way to get an estimate that may save you a little time.

Solving Quadratic Equations by Factoring

Source: Khan Academy