express x^2-4x+9 in the form (x-q)^2+y

divide the coefficient of the x term by 2-4/2=-2this is the value of the term, q.to find the term, y, simply square the value of q, and subtract it from the number term, which is in this case, 9(-2)^2=4. y=9-4=5putting it in the form asked for:=(x-2)²+5This is known as completing the square and is very useful for finding the roots of a quadratic equation. It is used when factorisation is not possible without the quadratic formula and you cant use a calculator.