Answer
Standard form: $f(t)=\frac{5}{2} t^2-10$
Vertex form: $f(t)=\frac{5}{2}(t-0)^2-10$
Factored form: $f(t)=\frac{5}{2}(t-2)(t+2)$.
Work Step by Step
14)The standard form is obtained by writing the right-hand side as two terms :
$$
\begin{aligned}
& f(t)=\frac{5 t^2-20}{2}\\
& f(t)=\frac{5}{2} t^2-10\\
\end{aligned}
$$
Complete the square to get the vertex form.
$$
\begin{aligned}
& f(t)=\frac{5}{2} t^2-10\\
& f(t)=\frac{5}{2}(t-0)^2-10 \\
\end{aligned}
$$
The factored form is
$$
\begin{aligned}
f(t) & =\frac{5 t^2-20}{2} \\
& =\frac{5}{2}\left(t^2-4\right) \\
& =\frac{5}{2}(t-2)(t+2)
\end{aligned}
$$
