Solving Quadratic Equations

Solving Quadratic Equations

1. Graphig method ii. Factorization Method iii. Completing Square Method iv. Using Quadratic Formula

I. Graphical Method

One way to determine the roots of a quadratic equation is to graph the related quadratic function. Write the equation in general form like:

$0 = x^{2} - 18x + 32$ dividing each side by 4.

The related function for this equation is

Notice that the function crosses the x- axis twice and the function has a degree of 2. These intercepts points are called the zero of a function. The x values, 2 and 16 are the roots of the equation $x^{2} - 18x + 32 = 0$ .

Example: Graph the related quadratic function $y = x^{2} - 2x - 15$ by finding and graphing the ordered pairs that satisfy the function.

Solution:

The graphs tells that the solutions are 3 and 5, where the curve intersects the x- axis.

II. Factoring Method

Another way of solving a quadratic equation is by factoring. The factoring method depends on the zero- product property.

Zero Product Property:

For any real number a and b, if ab = 0, then either a = 0 or b = 0.

i. To solve the quadratic equation by factorization first write it in standard form, then factorize the polynomial on the left-hand side of the equation. ii. Use zero product property. iii. Now solve linear equations and write solution set.

For example, to solve $x^{2} = 4$ by factorization we do the following steps:

Example: Factorize to solve the equations.

Solution: