Answer
Standard form: $g(s)=2 s^2-7 s-15$
Vertex form: $g(s)=2\left(s-\frac{7}{4}\right)^2-\frac{169}{8}$
Factored form: $g(s)=2(s-5)\left(s+\frac{3}{2}\right)$.
Work Step by Step
16)The standard form is :
$$
g(s)=(s-5)(2 s+3)=2 s^2+3 s-10 s-15=2 s^2-7 s-15
$$
Complete the square to get the vertex form.
$$
\begin{aligned}
g(s) & =2 s^2-7 s-15 \\
& =2\left(s^2-\frac{7}{2} s-\frac{15}{2}\right) \\
& =2\left(s^2-\frac{7}{2} s+\left(\frac{7}{4}\right)^2-\left(\frac{7}{4}\right)^2-\frac{15}{2}\right) \\
& =2\left(s-\frac{7}{4}\right)^2+2\left(-\frac{49}{16}-\frac{120}{16}\right) \\
& =2\left(s-\frac{7}{4}\right)^2-\frac{169}{8}
\end{aligned}
$$
The factored form is
$$
g(s)=(s-5)(2 s+3)=2(s-5)\left(s+\frac{3}{2}\right)
$$
