Question

What does the quadratic function y=x2−10x+9 look like when rewritten in the form f(x)= a(x-h)^2 +k?

Answer 1

$y=x^2-10x+9\\\\y=x^2-10x+25-16\\\\y=(x-5)^2-16$

Answer 2

We must use

$(a-b)^2=a^2-2ab+b^2\qquad(*)$

We have:

$y=x^2-10x+9=x^2-2(x)(5)+9=\underbrace{x^2-2(x)(5)+5^2}_{(*)}-5^2+9\\\\=(x-5)^2-25+9=\boxed{(x-5)^2-16}$

$a=1,\ h=5,\ k=-16$