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 expression
to express in the form
We might multiply this out to obtain
Now 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:
Hence
in completed square form is
Having completed the square we can solve the equation
Example: Complete the square for the expression
Hence solve the equation
Equating coefficients of
Equating coefficients of
Equating constant terms:
Hence
in completed square form is
Now we can solve
