#### Answer

$\color{blue}{f(x)=x^2+14x+45}$

#### Work Step by Step

RECALL:
The zeros of the quadratic function $f(x) =(x+a)(x+b)=0$ are $x=-a$ and $x=-b$.
The given quadratic function has the zeros $x=-5$ and $x=-9$.
Using the rule mentioned in the recall part above, then the function is:
$f(x)=(x+5)(x+9)
\\f(x)=x^2+x(9) + 5(x) + 5(9)
\\f(x)=x^2+9x+5x+45
\\\color{blue}{f(x)=x^2+14x+45}$