Thread: another quadratic equation

Let f(t) represent the number of new U.S. Hotel openings in the year that is t years since 1990. A possible equation for f is f(t)=-37.36t^2+559.33t-595.31

Find when f(t)=700. What does your result mean in terms of the situation?

Find the t-intercepts of f. What do the t-intercepts mean in terms of the situation.

This is what I have so far...

700= -37.36t^2+559.33t-595.31

Then I subtracted the 700 from the 595.31 which leaves me with this:
-37.36t^2+559.33t+104.69

a=37.36
b=559.33
c=104.69


then I set it up in quadratic formula..but now I am stuck.

Originally Posted by getnaphd

Let f(t) represent the number of new U.S. Hotel openings in the year that is t years since 1990. A possible equation for f is f(t)=-37.36t^2+559.33t-595.31

Find when f(t)=700. What does your result mean in terms of the situation?

Find the t-intercepts of f. What do the t-intercepts mean in terms of the situation.

This is what I have so far...

700= -37.36t^2+559.33t-595.31

Then I subtracted the 700 from the 595.31 which leaves me with this:
-37.36t^2+559.33t+104.69

a=37.36
b=559.33
c=104.69


then I set it up in quadratic formula..but now I am stuck.

Just relax and take it step by step. And always check your final answer.



<-- Watch the negative signs!

So



so








So either

or


I'll let you decide what the interpretation is.

As far as "t intercepts" are concerned, do you know what an "x intercept" is? Points on a function where it crosses the x axis. Well, t is taking the role of x here, so....

-Dan