A-LEVEL MATHEMATICS Topic : Completing the Square and Solving Quadratic Equations

Completing the square make it possible to find the maximum or 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 multiply 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