Question

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

Answer 1

ANSWER

When $f(x)=x^2-10x+9$ is written in the form $f(x)=a(x-h)^2+k$, it looks like $f(x)=(x-5)^2-16$

EXPLANATION

To write  $f(x)=x^2-10x+9$ in the form $f(x)=a(x-h)^2+k$, we have to complete the squares.

We add and subtract half the coefficient of $x$ square.

$f(x)=x^2-10x+(-5)^2-(-5)^2+9$

The first three terms of the function is now a perfect square.

$f(x)=(x-5)^2-25+9$

We now simplify rto obtain,

$\Rightarrow f(x)=(x-5)^2-16$