ANSWER
When [tex]f(x)=x^2-10x+9[/tex] is written in the form [tex]f(x)=a(x-h)^2+k[/tex], it looks like [tex]f(x)=(x-5)^2-16[/tex]
EXPLANATION
To write [tex]f(x)=x^2-10x+9[/tex] in the form [tex]f(x)=a(x-h)^2+k[/tex], we have to complete the squares.
We add and subtract half the coefficient of [tex]x[/tex] square.
[tex]f(x)=x^2-10x+(-5)^2-(-5)^2+9[/tex]
The first three terms of the function is now a perfect square.
[tex]f(x)=(x-5)^2-25+9[/tex]
We now simplify rto obtain,
[tex]\Rightarrow f(x)=(x-5)^2-16[/tex]
