Answer
$\color{blue}{f(x)=x^2+7.5x-4}$
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 $x=\frac{1}{2}$ and $x=-8$.
Using the rule mentioned in the recall part above, then the function is:
$f(x)=(x-\frac{1}{2})[x+8]
\\f(x)=(x-\frac{1}{2})(x+8)
\\f(x)=x(x)+x(8) - \frac{1}{2}(x) - \frac{1}{2}(8)
\\f(x)=x^2+8x-\frac{1}{2}x-4
\\\color{blue}{f(x)=x^2+7.5x-4}$
