## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{f(x)=x^2+7.5x-4}$
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: $f(x)=(x-\frac{1}{2})[x+8] \\f(x)=(x-\frac{1}{2})(x+8) \\f(x)=x(x)+x(8) - \frac{1}{2}(x) - \frac{1}{2}(8) \\f(x)=x^2+8x-\frac{1}{2}x-4 \\\color{blue}{f(x)=x^2+7.5x-4}$