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 expression
to express in the form
We might multip[ly 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
