Answer:
Step-by-step explanation:
DE given is
y''+8y'+15y=0, y(0)=0, y'(0)=1
Take Laplace on the DE
We get

Simplify to get
Y(s) = ![\frac{1}{2}[ {\frac{1}{s+3} -\frac{1}{s+5} }]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%20%7B%5Cfrac%7B1%7D%7Bs%2B3%7D%20-%5Cfrac%7B1%7D%7Bs%2B5%7D%20%7D%5D)
Take inverse

Answer:
(8, 15 and 17)
Step-by-step explanation:




I believe it is written as 0.43 <span />
We can use the vertex form of a quadratic,

, to find that

. Plugging

ordered pairs into g(x), we see that a = 1. For example, for

,

. Solving for a gives 1.