The value of Gentech stock is growing but beginning to level off. Use a quadratic function to model the data and consider the following questions:

a$)$ Let x$=$the number of years past $1982,$ and use regression to find a quadratic equation to model the data. Round the numbers in the equation to $3$ decimals places.

b$)$ Use the equation to predict the value of the stock in $2020.$ 

c$)$Use the equation to predict the year when the stock will reach a value of $$70$ per share, accurate to $1$ decimal place.

d$)$ Find the vertex and interpret its meaning in context of the data.  

 

Year: $1982,1985,1990,1993,1998,2002$

Value: $$14,20,$ $$26,$ $$40\mathrm{.}40,$ $$46\mathrm{.}60,$ $$57\mathrm{.}60,$ $$64\mathrm{.}20$