Completing the Square and Solving Quadratic Equations

Completing the square make it possible to find the maximum of minimum value of a quadratic function without sketching it., or to solve quadratic equations without using the quadratic formula.. We start with an expressionto express in the form

We might multip[ly this out to obtainNow we equateto this and solve for the coefficients a, b, c.

Example: Complete the square for the expression

Equating coefficients of

Equating coefficients of

Equating constant terms:

Hencein completed square form is

Having completed the square we can solve the equation

Example: Complete the square for the expressionHence solve the equation

Equating coefficients of

Equating coefficients of

Equating constant terms:

Hencein completed square form is

Now we can solve